453 results

expression - finite combination of symbols

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m months.
Set up the cost function C(m) where m is the number of months you rent:
C(m) = Monthly membership fee * m + initial fee
[B]C(m) = 30m + 100[/B]

(n^2)^3 without exponents

(n^2)^3 without exponents
This expression evaluates to:
n^(2 *3)
n^6
To write this without exponents, we expand n times itself 6 times:
[B]n * n * n * n * n * n
[MEDIA=youtube]zVAlzX9oHOQ[/MEDIA][/B]

-3x to the negative one power

-3x to the negative one power
Raising to a negative power means taking 1 over the same expression to the positive power"
(-3x)^-1 = 1/-3x = [B]-1/3x[/B]

-65 times the difference between a number and 79 is equal to the number plus 98

-65 times the difference between a number and 79 is equal to the number plus 98
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x:
x - 79
Next, -65 times the difference between a number and 79 means we multiply our result above by -65:
-65(x - 79)
The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x:
x + 98
Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98:
-65(x - 79) = x + 98[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get:
x = [B]76.31818[/B]

1/2 of x and 10 is 30. Find the x.

1/2 of x and 10 is 30. Find the x.
x and 10 means we add:
x + 10
1/2 of this:
1/2(x + 10)
The phrase is means equal to, so we set 1/2(x + 10) equal to 30 for our algebraic expression
[B]1/2(x + 10) = 30[/B]

1/4 of the difference of 6 and a number is 200

1/4 of the difference of 6 and a number is 200
Take this [B]algebraic expression[/B] in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The difference of 6 and a number means we subtract x from 6: 6 - x
[*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4
[*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200
[/LIST]
[B](6 - x)/4 = 200[/B]

1/6 of n subtracted from 3

1/6 of n subtracted from 3
1/6 of n:
n/6
Subtracted from 3 means we subtract this expression from 3:
[B]3 - n/6[/B]

10 divided by the sum of 4 and u

10 divided by the sum of 4 and u
Take this algebraic expression in parts:
The sum of 4 and u means we add 4 to u:
4 + u
Next, we divide 10 by this sum:
[B]10/(4 + u)[/B]

10 times a number is 420

10 times a number is 420
A number denotes an arbitrary variable, let's call it x.
10 times a number:
10x
The phrase is means equal to, so we set 10x equal to 420
[B]10x = 420 <-- This is our algebraic expression
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL]
We get x = 42

108 times a, reduced by 147 is k subtracted from 56

108 times a, reduced by 147 is k subtracted from 56
Take this algebraic expression in pieces:
Step 1: 108 times a:
108a
Step 2: Reduced by means subtract, so we subtract 47 from 108a:
108a - 47
Step 3: ksubtracted from 56:
56 - k
Step 4: The phrase [I]is[/I] means equal to, so we set 108a - 47 equal to 56 - k
[B]108a - 47 = 56 - k
[MEDIA=youtube]KrY6uzKeeB0[/MEDIA][/B]

12 divided into groups of s

12 divided into groups of s
We build our algebraic expression as follows:
[B]12/s[/B]

12 plus 6 times a number is 9 times the number

12 plus 6 times a number is 9 times the number
The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
6 times a number is written as:
6x
12 plus 6 times the number means we add 6x to 12:
12 + 6x
9 times a number is written as:
9x
The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x
[B]12 + 6x = 9x <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get:
x = [B]4[/B]

12 plus the product of 4 and a number is greater than 72

A number means an arbitrary variable, let's call it x.
The product of 4 and a number is 4x.
12 plus that product is 4x + 12
Is greater than means an inequality, so we set the entire expression greater than 72
4x + 12 > 72

13 more than x is greater than 14

13 more than x means we add:
x + 13
This expression is greater than 14, so we write an inequality:
x + 13 > 14

132 is 393 multiplied by y

132 is 393 multiplied by y
393 multiplied by y
393y
The word [I]is[/I] means equal to, so we set 393y equal to 132 as our algebraic expression
[B]393y = 132
[/B]
If you need to solve for y, use our [URL='http://www.mathcelebrity.com/1unk.php?num=393y%3D132&pl=Solve']equation calculator[/URL]

15 added to the quotient of 8 and a number is 7.

15 added to the quotient of 8 and a number is 7.
Take this algebraic expression in pieces:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The quotient of 8 and a number: 8/x
[*]15 added to this quotient: 8/x + 15
[*]The word [I]is[/I] means an equation, so we set 8/x + 15 equal to 7
[/LIST]
[B]8/x + 15 = 7[/B]

16 decreased by 3 times the sum of 3 and a number

16 decreased by 3 times the sum of 3 and a number
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The sum of 3 and a number: 3 + x
[*]3 times the sum: 3(3 + x)
[*]16 decreased by... means we subtract 3(3 + x) from 16
[/LIST]
[B]3(3 + x) from 16[/B]

175 students separated into n classes is 25

175 students separated into n classes is 25
[U]Divide 175 by n[/U]
175/n
[U]The word [I]is[/I] means equal to, so set this expression equal to 25[/U]
175/n = 25
[U]Cross multiply[/U]
25n = 175
[U]Divide each side by 25[/U]
[B]n = 7[/B]

18 seconds faster than Tina’s time

18 seconds faster than Tina’s time
Let Tina's time be t. Speaking in terms of time, faster means less. So we have an algebraic expression of:
[B]t - 18[/B]

19 decreased by the absolute value of c

19 decreased by the absolute value of c
Take this algebraic expression in parts:
[LIST]
[*]Absolute value of c: |c|
[*]19 decreased by the absolute value of c is found by subtracting |c| from 19
[/LIST]
[B]19 - |c|[/B]

2 - 8 ÷ (2^4 ÷ 2) =

Using PEDMAS:
2^4 = 16
New expression:
2 - 8 ÷ (16 ÷ 2)
(16 ÷ 2)= 8
New Expression
2 - 8 ÷ 8
8 ÷ 8 = 1
New Expression
2 - 1
2 - 1 = [B]1
[MEDIA=youtube]IyRW29YtOZw[/MEDIA][/B]

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the 2 cards represent the same number?
If they have the same number, we set them equal to each other and solve for y:
5y - 2 = 3y + 10
To solve for y, we [URL='http://5y - 2 = 3y + 10']type this expression in our search engine [/URL]and we get:
y = [B]6[/B]

2 times a number equals that number plus 5

2 times a number equals that number plus 5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
2 times a number means we multiply 2 by x:
2x
That number plus 5 means we add 5 to the number x
x + 5
The phrase [I]equals[/I] means we set both expressions equal to each other
[B]2x = x + 5[/B] <-- This is our algebraic expression
If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get:
[B]x = 5[/B]

2 times the sum of 3 and 5 divided by 10

2 times the sum of 3 and 5 divided by 10
The sum of 3 and 5 is written as:
3 + 5
2 times this sum:
2(3 + 5)
Then, we divide this by 10:
[B]2(3 + 5)/10[/B]
[B][/B]
If the problem asks you to simplify this, you [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=2%283%2B5%29%2F10&pl=Perform+Order+of+Operations']type this expression into our search engine[/URL] and get:
[B]1.6[/B]

2 times the sum of 7 times a number and 4

2 times the sum of 7 times a number and 4
This is an algebraic expression. Let's take it in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]7 times a number means we multiply x by 7: 7x
[*]The sum of 7 times a number and 4 means we add 4 to 7x: 7x + 4
[*]Finally, we multiply the sum in #3 by 2
[/LIST]
Build our final algebraic expression:
[B]2(7x + 4)[/B]

20 yards longer than p

20 yards longer than p
We want to build an algebraic expression. Longer means we add 20 to p:
[B]p + 20[/B]

217 times u, reduced by 180 is the same as q

217 times u, reduced by 180 is the same as q.
Take this algebraic expression pieces:
Step 1: 217 times u
We multiply the variable u by 217
217u
Step 2: reduced by 180
Subtract 180 from 217u
217u - 180
The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q
[B]217u - 180 = q[/B]

223 subtracted from the quantity 350 times a is equal to b

223 subtracted from the quantity 350 times a is equal to b
Take this algebraic expression in parts:
[LIST]
[*]the quantity 350 times a: 350a
[*]223 subtracted from the quantity: 350a - 223
[*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b
[/LIST]
[B]350a - 223 = b[/B]

231 is 248 subtracted from the quantity h times 128

231 is 248 subtracted from the quantity h times 128
Let's take this algebraic expression in parts:
[LIST=1]
[*]h times 128: 128h
[*]24 subtracted from this: 128h - 248
[*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231
[/LIST]
[B]128h - 248 = 231[/B] <-- This is our algebraic expression
If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get:
h = [B]3.742[/B]

249 equals 191 times c, decreased by 199

249 equals 191 times c, decreased by 199
[U]Take this in pieces:[/U]
191 times c: 191c
The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199
We set this expression equal to 249:
[B]191c - 199 = 249[/B] <-- This is our algebraic expression
If you want to solve for c, type this equation into the search engine and we get:
[B]c = 2.346[/B]

2x decreased by 15 is equal to -27

2x decreased by 15 is equal to -27
The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x:
2x - 15
The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27
[B]2x - 15 = -27 [/B] <-- This is our algebraic expression
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].

2x plus 4 increased by 15 is 57

2x plus 4 increased by 15 is 57
Take this algebraic expression in parts:
[LIST]
[*]2x plus 4: 2x + 4
[*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19
[*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57:
[/LIST]
Our final algebraic expression is:
[B]2x + 19 = 57
[/B]
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get
x = [B]19[/B]

3 is subtracted from the square of x

3 is subtracted from the square of x
Let's take this algebraic expression in two parts:
Part 1: The square of x means we raise x to the power of 2:
x^2
Part 2: 3 is subtracted means we subtract 3 from x^2
[B]x^2 - 3[/B]

3 more than the product of 7 and a number x is less than 26

The product of 7 and a number x is written as 7x.
3 more than that product is written as 7x + 3.
Finally, that entire expression is less than 26, so we have:
7x + 3 < 26 as our algebraic expression.
[MEDIA=youtube]ESuHovml5WQ[/MEDIA]

3 times a number increased by 1 is between -8 and 13

3 times a number increased by 1 is between -8 and 13.
Let's take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Part 2 - 3 times this number means we multiply x by 3:
3x
Part 3 - Increased by 1 means we add 1 to 3x:
3x + 1
The phrase [I]between[/I] means we have an inequality:
[B]-8 <= 3x + 1 <=13[/B]

3 times larger than the sum of 4 and 9

The sum of 4 and 9:
4 + 9
3 times larger than this sum
[B]3(4 + 9) <-- This is our algebraic expression
[/B]
Evaluating this amount:
3(13)
[B]39[/B]

3 times the difference of x and 5 is 15

The difference of x and 5 means we subtract:
x - 5
3 times the difference means we multiply (x - 5) by 3
3(x - 5)
Is, means equal to, so we set our expression equal to 15
[B]3(x - 5) = 15
[/B]
If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]

3 times the square of a number x minus 12

3 times the square of a number x minus 12.
Build the algebraic expression piece by piece:
[LIST]
[*]Square of a number x: x^2
[*]3 times this: 3x^2
[*]Minus 12: [B]3x^2 - 12[/B]
[/LIST]

3 times the sum of x and 9y

3 times the sum of x and 9y
The sum of x and 9y means we add 9y to x:
x + 9y
Now we take this sum, and multiply by 3 to get our final algebraic expression:
3(x + 9y)

3 times the width plus 2 times the length

3 times the width plus 2 times the length
Let w be the width
Let l be the length
We have an algebraic expression of:
[B]3w + 2l[/B]

3 times x minus y is 5 times the sum of y and 2 times x

3 times x minus y is 5 times the sum of y and 2 times x
Take this algebraic expression in pieces:
3 times x:
3x
Minus y means we subtract y from 3x
3x - y
The sum of y and 2 times x mean we add y to 2 times x
y + 2x
5 times the sum of y and 2 times x:
5(y + 2x)
The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x)
[B]3x - y = 5(y + 2x)[/B]

30% larger then 1/3 of twice q

30% larger then 1/3 of twice q
Take this algebraic expression in 3 parts:
[LIST=1]
[*]Twice q means multiply q by 2: 2q
[*]1/3 of twice q means we multiply 2q in Step 1 by 1/3: 2q/3
[*]30% larger means we multiply 2q/3 in step 2 by 1.3, since 30% = 0.3: 1.3(2q/3)
[/LIST]
[B]1.3(2q/3)[/B]

300 reduced by 5 times my age is 60

300 reduced by 5 times my age is 60
Let my age be a. We have:
5 times my age = 5a
300 reduced by 5 times my age means we subtract 5a from 300:
300 - 5a
The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression:
[B]300 - 5a = 60
[/B]
If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get:
a = [B]48[/B]

309 is the same as 93 subtracted from the quantity f times 123

309 is the same as 93 subtracted from the quantity f times 123.
The quantity f times 123:
123f
Subtract 93:
123f - 93
The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309
[B]123f - 93 = 309[/B] <-- This is our algebraic expression
If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.

324 times z, reduced by 12 is z

324 times z, reduced by 12 is z.
Take this algebraic expression in pieces:
324 [I]times[/I] z means we multiply 324 by the variable z.
324z
[I]Reduced by[/I] 12 means we subtract 12 from 324z
324z - 12
The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z
[B]324z - 12 = z [/B] <-- This is our algebraic expression

339 equals 303 times w, minus 293

339 equals 303 times w, minus 293
Take this algebraic expression in pieces:
303 times w:
303w
Minus 293:
303w - 293
The phrase [I]equals[/I] means we have an equation. We set 303w - 293 = 339
[B]303w - 293 = 339[/B] <-- This is our algebraic expression
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=303w-293%3D339&pl=Solve']we type this equation into our search engine[/URL] to get:
[B]w = 2.086[/B]

35 added to n is greater than or equal to the sum of k and 21

35 added to n is greater than or equal to the sum of k and 21
Take this algebraic expression in 3 parts:
[LIST=1]
[*]35 added to n means we have a sum: n + 35
[*]The sum of k and 21 means we add 21 to k: k +21
[*]The phrase [I]greater than or equal to[/I] means an inequality using this sign (>=), so we write this as follows:
[/LIST]
[B]n + 35 >= k + 21[/B]

3f,subtract g from the result, then divide what you have by h

3f,subtract g from the result, then divide what you have by h
Take this algebraic expression in pieces:
3f subtract g means we subtract the variable g from the expression 3f:
3f - g
Divide what we have by h, means we take the result above, 3f - g, and divide it by h:
[B](3f - g)/h[/B]

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5
This is an algebraic expression. Let's take this algebraic expression in 5 parts:
[LIST=1]
[*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1
[*]2 times the sum of 2x and 1: 2(2x + 1)
[*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x
[*]The sum of 2 and 5 means we add 5 to 2: 2 + 5
[*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4
[/LIST]
Our algebraic expression is:
[B]2(2x + 1) - 3x = 2 + 5[/B]
Now, some problems may ask you to simplify. In this case, we multiply through and group like terms:
4x + 2 - 3x = 7
[B]x + 2 = 7 <-- This is our simplified algebraic expression
[/B]
Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get:
x =[B] 5
[MEDIA=youtube]3hzyc2NPCGI[/MEDIA][/B]

3x to the power 2n

3x to the power 2n
We take the expression 3x raise it to the power of 2n
[B](3x)^2n[/B]

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many te

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many teaspoons of vinegar?
Set up a proportion where x is the number of teaspoons of vinegar in the second scenario:
4/6 = 20/x
[URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=20&den1=6&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']Plug that expression into the search engine to get[/URL]
[B]x = 30[/B]

4 times 8 to the sixth power

4 times 8 to the sixth power
8 to the 6th power:
8^6
4 times this amount:
4 * 8^6
To evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=4%2A8%5E6&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
1,048,576

4 times a number added to 8 times a number equals 36

4 times a number added to 8 times a number equals 36
Let [I]a number[/I] be an arbitrary variable, let us call it x.
4 times a number:
4x
8 times a number:
8x
We add these together:
4x + 8x = 12x
We set 12x equal to 36 to get our final algebraic expression of:
[B]12x = 36
[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/1unk.php?num=12x%3D36&pl=Solve']type this algebraic expression into our search engine[/URL] and get:
x = [B]3[/B]

4 times a number is the same as the number increased by 78

4 times a number is the same as the number increased by 78.
Let's take this algebraic expression in parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]4 times a number is written as 4x
[*]The number increased by 78 means we add 78 to x: x + 78
[*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3
[/LIST]
[B]4x = x + 78[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get:
x = 26

4 times b increased by 9 minus twice y

4 times b increased by 9 minus twice y
Take this algebraic expression in parts:
Step 1: 4 times b means we multiply the variable b by 4:
4b
Step 2: Increased by 9 means we add 9 to 4b:
4b + 9
Step 3: Twice y means we multiply the variable y by 2:
2y
Step 4: The phrase [I]minus[/I] means we subtract 2y from 4b + 9
[B]4b + 9 - 2y[/B]

4 times the number of cows plus 2 times the number of ducks

4 times the number of cows plus 2 times the number of ducks
Let c be the number of cows. Let d be the number of ducks. We've got an algebraic expression below:
[B]4c + 2d[/B]

48 is the difference of Chrissys height and 13 .

48 is the difference of Chrissys height and 13 .
Let Chrissy's height = h.
The difference of the height and 13 is h - 13.
We set this expression equal to 48:
[B]h - 13 = 48
[/B]
Note: To solve this, [URL='http://www.mathcelebrity.com/1unk.php?num=h-13%3D48&pl=Solve']paste this problem into the search engine[/URL].

4subtractedfrom6timesanumberis32

4 subtracted from 6 times a number is 32.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times this number means we multiply by x by 6
6x
4 subtracted from this expression means we subtract 4
6x - 4
The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32
[B]6x - 4 = 32
[/B]
If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].

5 added to x is 11

x + 5 = 11 for the algebraic expression.
Plug that into the [URL='http://www.mathcelebrity.com/1unk.php?num=x%2B5%3D11&pl=Solve']search engine[/URL], and solve for x.
x = 6.

5 added to xis 11

5 added to x means we use the plus sign for a sum.
x + 5
"is" means equals, so we set that equal to 11.
x + 5 = 11 <-- This is our algebraic expression.

5 diminished by twice the sum of a and b

5 diminished by twice the sum of a and b
Take this algebraic expression in parts:
[LIST]
[*]The sum of a and b: a + b
[*]Twice the sum means we multiply a + b by 2: 2(a + b)
[*]5 diminished by twice the sum means we subtract 2(a + b) from 5
[/LIST]
[B]5 - 2(a + b)[/B]

5 more than the reciprocal of a number

5 more than the reciprocal of a number
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of this number means we divide 1 over x:
1/x
5 more means we add 5 to 1/x
[B]1/x + 5[/B]

5 more than twice the cube of a number

5 more than twice the cube of a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The cube of a number means we raise it to a power of 3
x^3
Twice the cube of a number means we multiply x^3 by 2
2x^3
5 more than twice the cube of a number means we multiply 2x^3 by 5
5(2x^3)
Simplifying, we get:
10x^3

5 subtracted from 3 times a number is 44

5 subtracted from 3 times a number is 44.
The problem asks for an algebraic expression.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times this number is 3x.
5 subtracted from this is written as 3x - 5.
The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44
[B]3x - 5 = 44[/B]

5 times a number increased by 4 is divided by 6 times the same number

5 times a number increased by 4 is divided by 6 times the same number
Take this algebraic expression in parts.
Part 1: 5 times a number increased by 4
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x
[*]5 times the number means multiply x by 5: 5x
[*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4
[/LIST]
Part 2: 6 times the same number
[LIST]
[*]From above, [I]a number[/I] is x: x
[*]6 times the number means we multiply x by 6: 6x
[/LIST]
The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator.
[B](5x + 4)/6x[/B]

5 times g reduced by the square of h

5 times g reduced by the square of h
Take this algebraic expression in pieces:
[LIST=1]
[*]5 times g means we multiply g by 5: 5g
[*]The square of h means we raise h to the 2nd power: h^2
[*]5 times g reduced by the square of h means we subtract h^2 from 5g:
[/LIST]
[B]5g - h^2[/B]

50 is more than the product of 4 and w

50 is more than the product of 4 and w
Take this algebraic expression in pieces:
The product of 4 and w mean we multiply the variable w by 4:
4w
The phrase [I]is more than[/I] means an inequality using the (>) sign, where 50 is greater than 4w:
[B]50 > 4w[/B]

54 is the sum of 15 and Vidyas score

54 is the sum of 15 and Vidyas score.
Let Vida's score be s.
The sum of 15 and s:
s + 15
When they say "is", they mean equal to, so we set s + 15 equal to 54. Our algebraic expression is below:
[B]s + 15 = 54
[/B]
To solve this equation for s, use our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B15%3D54&pl=Solve']equation calculator[/URL]

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.
Sum of 24 and Julie's score:
24 + J
The phrase [I]is[/I] means an equation, so we set 24 + J equal to 54 to get an algebraic expression:
[B]24 + J = 54[/B]

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.
The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16:
d + 16
The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59
d + 16 = 59 <-- [B]This is our algebraic expression[/B]
Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]:
d = [B]43[/B]

6 subtracted from the product of 5 and a number is 68

6 subtracted from the product of 5 and a number is 68
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The product of 5 and this number is:
5x
We subtract 6 from 5x:
5x - 6
The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68
[B]5x - 6 = 68[/B]

6 times a number multiplied by 3 all divided by 4

6 times a number multiplied by 3 all divided by 4
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]6 times a number: 6x
[*]Multiplied by 3: 3(6x) = 18x
[*]All divided by 4: 18x/4
[/LIST]
We can simplify this:
We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is:
[B]9x/2[/B]

6 times a number, x, is at least 22.

6 times a number, x, is at least 22.
6 times a number x:
6x
The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality:
[B]6x >= 22[/B] <-- This is our algebraic expression
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get:
[B]x >= 3.666667[/B]

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number
We've got two algebraic expressions here. Let's take it in parts:
Term 1:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal is 1/x
Multiply this by 6: 6/x
Term 2:
Reciprocal of 7: 1/7
2 times this: 2/7
We set these terms equal to each other:
6/x = 2/7
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]x = 21[/B]

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .
This is an algebraic expression. Let's take it in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number x means we divide 1 over x:
1/x
6 times the reciprocal means we multiply 6 by 1/x:
6/x
The reciprocal of 7 means we divide 1/7
1/7
3 times the reciprocal means we multiply 1/7 by 3:
3/7
Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7
[B]6/x = 3/7[/B] <-- This is our algebraic expression
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get:
x = 14

6 times the sum of a number and 3 is equal to 42. What is this number?

6 times the sum of a number and 3 is equal to 42. What is this number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 3 means we add 3 to x:
x + 3
6 times the sum:
6(x + 3)
The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of:
[B]6(x + 3) = 42[/B]
[B][/B]
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get:
x = [B]4[/B]

6 times the sum of a number and 5 is 16

6 times the sum of a number and 5 is 16
A number represents an arbitrary variable, let's call it x
x
The sum of x and 5
x + 5
6 times the sum of x and 5
6(x + 5)
Is means equal to, so set 6(x + 5) equal to 16
[B]6(x + 5) = 16 <-- This is our algebraic expression
Solve for x[/B]
Multiply through:
6x + 30 = 16
Subtract 30 from each side:
6x - 30 + 30 = 16 - 30
6x = -14
Divide each side by 6
6x/6 = -14/6
Simplify this fraction by dividing top and bottom by 2:
x = [B]-7/3
[MEDIA=youtube]oEx5dsYK7DY[/MEDIA][/B]

60 percent of a number minus 17 is -65

60 percent of a number minus 17 is -65
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have:
0.6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is:
0.6x
Minus 17:
0.6x - 17
The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of:
[B]0.6x - 17 = -65[/B]
[B][/B]
If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]:
[B]x = -80[/B]

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.
The phrase [I]difference between[/I] means we subtract 44 from a:
a - 44
The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64
[B]a - 44 = 64 <-- This is our algebraic expression
[/B]
If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get:
[B]a = 108[/B]

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44
Difference between Sarah's age (a) and 44 (Assuming Sarah is older than 44):
a - 44
4 times the difference:
4(a - 44)
The word [I]is[/I] means equal to, so we set 4(a - 44) equal to 64 to get our algebraic expression:
[B]4(a - 44) = 64[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4%28a-44%29%3D64&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]60[/B]

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is written as -2x.
Less means subtract, so we have 7 less than this is -2x - 7.
Finally, greater than or equal to is >=, so our expression becomes:
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less than that means we subtract 7:
-2x - 7
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less means we subtract, so 7 less than that is -2x - 7.
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

7 less than -2 times a number x is greater than or equal to 41
-2 times a number x
-2x
7 less than this
-2x - 7
Now we set this expressions greater than or equal to 41
[B]-2x - 7 >= 41[/B]

7 multiplied by the quantity 7 take away 6

7 multiplied by the quantity 7 take away 6
Take this algebraic expression in pieces:
[LIST]
[*]7 take away 6: 7 - 6
[*]7 multiplied by the quantity: [B]7(7 - 6)[/B]
[/LIST]
This is our algebraic expression.
If you need to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=7%287-6%29&pl=Perform+Order+of+Operations']type it in the search engine[/URL] and we get;
[B]7[/B]

7 times a number increased by 4 times the number

7 times a number increased by 4 times the number
Let [I]a number[/I] and [I]the number[/I] be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
[LIST]
[*]7 times a number: 7x
[*]4 times the number: 4x
[*]The phrase [I]increased by[/I] means we add 4x to 7x:
[*]7x + 4x
[*]Simplifying, we get: (7 + 4)x
[*][B]11x[/B]
[/LIST]

7 times a number is the same as 12 more than 3 times a number

7 times a number is the same as 12 more than 3 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[B][U]Algebraic Expression 1:[/U][/B]
7 times a number means we multiply 7 by x:
7x
[B][U]Algebraic Expression 2:[/U][/B]
3 times a number means we multiply 3 by x:
3x
12 more than 3 times a number means we add 12 to 3x:
3x + 12
The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12
[B]7x = 3x + 12[/B] <-- Algebraic Expression

7 times a positive number n is decreased by 3, it is less than 25

7 times a positive number n is decreased by 3, it is less than 25
7 times a positive number n:
7n
Decreased by 3:
7n - 3
The phrase [I]it is less than [/I]means an inequality. So we relate 7n - 3 less than 25 using the < sign to get our algebraic expression of:
[B]7n - 3 < 25[/B]

7 times the cube of the sum of x and 8

7 times the cube of the sum of x and 8
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of x and 8 means we add 8 to x: x + 8
[*]The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3
[*]7 times this cubed sum means we multiply (x + 8)^3 by 7:
[/LIST]
[B]7(x + 8)^3[/B]

7 times the number of lions plus 4 times the number of tigers

7 times the number of lions plus 4 times the number of tigers
Let the number of lions be l
Let the number of tigers be t
We have an algebraic expression of:
[B]7l + 4t[/B]

72 pounds and increases by 3.9 pounds per month

72 pounds and increases by 3.9 pounds per month
Let m be the number of months. We write the algebraic expression below:
[B]3.9m + 72[/B]

75% of x is 25 dollars and 99 cents

75% of x is 25 dollars and 99 cents
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=75&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Since 75%[/URL] is 0.75 as a decimal, we rewrite this as an algebraic expression:
0.75x = 25.99
If we want to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75x%3D25.99&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]34.65[/B]

76 subtracted from p is equal to the total of g and 227

76 subtracted from p is equal to the total of g and 227
We've got two algebraic expressions. Take them in pieces:
Part 1:
76 subtracted from p
We subtract 76 from the variable p
p - 76
Part 2:
The total of g and 227
The total means a sum, so we add 227 to g
g + 227
Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other:
[B]p - 76 = g + 227[/B]

8 increased by the product of a number and 7 is greater than or equal to -18

Take this in parts:
First, the phrase, "a number" means we pick an arbitrary variable, let's call it x.
The product of a number and 7 is 7x.
8 increased by the product of 7x means we add them together.
7x + 8
Finally that entire expression is greater than [U]or equal to[/U] -18
[B]7x + 8 >=-18[/B]

8 is subtracted from the square of x

8 is subtracted from the square of x
Take this algebraic expression in parts:
[LIST]
[*]The square of x means we raise x to the power of 2: x^2
[*]8 subtracted from the square of x is found by subtracting 8 from x^2
[/LIST]
[B]x^2 - 8[/B]

8 less thantriplethedifferenceof2xand6

8 less than triple the difference of 2x and 6
The [I]difference[/I] of 2x and 6 means we [B]subtract[/B] 6 from 2x
2x - 6
[I]Triple[/I] this difference means we [B]multiply by 3[/B]
3(2x - 6)
8 [I]less[/I] means we [B]subtract 8 from this expression
3(2x - 6) - 8[/B]

8 more than the product of x and 2 equals 4

8 more than the product of x and 2 equals 4
The product of x and 2:
2x
8 more than this, means we add 8:
2x + 8
Set this equal to 4:
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B8%3D4&pl=Solve']2x + 8 = 4[/URL] <-- Algebraic expression
to solve for x, type this into the search engine and we get [B]x = -2[/B].

8 more than twice a number is less than 6 more than the number

8 more than twice a number is less than 6 more than the number.
This is an algebraic expression, let's take it in pieces...
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
8 more than twice a number:
Twice a number means multiply x by 2: 2x
Then add 8: 2x + 8
6 more than the number, means we add 6 to x
x + 6
The phrase [I]is less than[/I] means an inequality, where we set 2x + 8 less than x + 6
[B]2x + 8 < x + 6[/B]

8 taken away from y

8 taken away from y
This is an algebraic expression. The phrase [I]taken away[/I] means we subtract 8 from y:
[B]y - 8[/B]

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]8(n - 2) [I]difference means we subtract[/I]
[*]3(n + 3) [I]sum means we add[/I]
[/LIST]
The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression:
8(n - 2) = 3(n + 3)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that:
n =[B] 5[/B]

8 times the sum of 5 times a number and 9

8 times the sum of 5 times a number and 9
Take this algebraic expression in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
5 times a number means:
5x
The sum of this and 9 means we add 9 to 5x:
5x + 9
Now we multiply 8 times this sum:
[B]8(5x + 9)[/B]

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4.
Build our two algebraic expressions first:
9 divided by the sum of x and 4
9/(x + 4)
6 divided by x minus 4
6/(x - 4)
The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other:
[B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, we cross multiply:
9(x - 4) = 6(x + 4)
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]20[/B]

9 is one-third of a number x

9 is one-third of a number x
A number x can be written as x
x
one-third of a number x means we multiply x by 1/3:
x/3
The phrase [I]is[/I] means an equation, so we set 9 equal to x/3 to get our final algebraic expression of:
[B]x/3 = 9[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=9&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this algebraic expression into our search engine[/URL] and you get:
[B]x = 27[/B]

9 is the sum of thrice x and y

9 is the sum of thrice x and y
Thrice x means multiply x by 3:
3x
Sum of this and y:
3x + y
Now we set this expression equal to 9:
[B]3x + y = 9[/B]

9 less than 5 times a number is 3 more than 2x

9 less than 5 times a number is 3 more than 2x
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
5 times a number means we multiply x by 5:
5x
9 less than 5x means we subtract 9 from 5x:
5x - 9
3 more than 2x means we add 3 to 2x:
2x + 3
The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3:
[B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B]
[B][/B]
If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get:
x = [B]4[/B]

9 subtracted from the product of 3 and a number is greater than or equal to 16

9 subtracted from the product of 3 and a number is greater than or equal to 16
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The product of 3 and a number means we multiply 3 times x: 3x
[*]9 subtracted from the product: 3x - 9
[*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16
[/LIST]
Our algebraic expression (inequality) becomes:
[B]3x - 19 >= 16[/B]

9 times a number is that number minus 3

9 times a number is that number minus 3
Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given:
9 times a number is 9x
The number minus 3 is x - 3
The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]:
[B]9x = x - 3[/B]
To solve for x, we type this equation into our search engine and we get:
x = [B]-0.375 or -3/8[/B]

A bowl contains 45 oranges. If ⅔ of the oranges are bad; how many are good?

A bowl contains 45 oranges. If ⅔ of the oranges are bad; how many are good?
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=2%2F3&pl=Subtract']fraction operator calculator[/URL], we see that:
1 - 2/3 = 1/3 of the oranges are good.
We want 1/3 of 45. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/3&pl=Multiply']Typing this expression into our search engine[/URL], we get:
[B]15 good oranges[/B]

A boy has m mangoes. He sells three of them write down an expression to represent how much he now ha

A boy has m mangoes. He sells three of them write down an expression to represent how much he now has.
When the boy sells the mangos, he has less. So we subtract 3 from m to get:
[B]m - 3[/B]

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours.
Distance = rate * time, so we have:
Distance = 40km/h * h
Distance = [B]40h[/B]

A coat is on sale for 35% off. The regular price of the coat is p. Write and simplify and expression

A coat is on sale for 35% off. The regular price of the coat is p. Write and simplify and expression to represent the sale price of the coat. Show your work.
The Sale price of the coat is:
S = p(1 - 0.35) <-- Since 35% is 0.35 as a decimal
[B]S = 0.65p[/B]

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v to find the volume. What was the volume of the tank?
1/2 foot = 6 inches
v = (6)^3
v = [B]216 cubic inches[/B]

A customer withdrew $100 from a bank account. The customer then deposited $33 the next day. Write an

A customer withdrew $100 from a bank account. The customer then deposited $33 the next day. Write and then evaluate an expression to show the net effect of these transactions.
Withdrawals are negative since we take money away
Deposits are positive since we add money
So we have:
[LIST]
[*]100 withdrawal = -100
[*]33 deposit = +33
[/LIST]
Our balance is:
-100 + 33 = [B]-67 net[/B]

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
Let the number of drinks be d. Let the number of salads be s. We're given two equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d + s = 209
[/LIST]
We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides:
d + s - s = 209 - s
Cancel the s's, we get:
d = 209 - s
So we have the following system of equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d = 209 - s
[/LIST]
Substitute equation (2) into equation (1) for d:
2(209 - s) + 6.50s = 836.50
Multiply through to remove the parentheses:
418 - 2s + 6.50s = 836.50
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]:
s = [B]93[/B]

A football team gained 4 yards on a play,lost 8 on the next play ,then gained 2 yards on the third p

A football team gained 4 yards on a play,lost 8 on the next play ,then gained 2 yards on the third play write and addition expression
Gains are expressed with positives (+) and losses are expressed with negatives (-):
[LIST]
[*]Gained 4 years: +4
[*]Lost 8 on the next play: -8
[*]Gained 2 yards on the third play: +2
[/LIST]
Expression:
[B]+4 - 8 + 2 = -2[/B]

A group of p people sold a car for $5000. Write an expression in terms of p for how much money each

A group of p people sold a car for $5000. Write an expression in terms of p for how much money each person gets.
Each person gets:
[B]5000/p[/B]

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet.

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet. Write an expression to represent this situation. Then determine and interpret the sum.
[LIST]
[*]Start at +785 feet
[*]Descend 570 feet means using a minus sign -570
[*]Ascend 595 feet means using a plus sign +595
[/LIST]
[U]Calculate the sum:[/U]
+785 - 570 + 595
[B]+810[/B]

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hour

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hours it takes the machine to print 1265 posters.
Let h be the number of hours. We're given the following expression for the printing output of the machine:
230h
The questions asks for how long (h) to print 1265 posters, so we setup the equation:
230h = 1265
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=230h%3D1265&pl=Solve']type this equation into our math engine[/URL] and we get:
h = [B]5.5 hours[/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?
Declare variables:
[LIST]
[*]Let a be the number of adult's tickets
[*]Let c be the number of children's tickets
[/LIST]
Cost = Price * Quantity
We're given two equations:
[LIST=1]
[*]a + c = 20
[*]15a + 10c = 225
[/LIST]
Rearrange equation (1) in terms of a:
[LIST=1]
[*]a = 20 - c
[*]15a + 10c = 225
[/LIST]
Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
15(20 - c) + 10c = 225
Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225
We first need to simplify the expression removing parentheses
Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
15 * 20 = (15 * 20) = 300
15 * -c = (15 * -1)c = -15c
Our Total expanded term is 300-15c
Our updated term to work with is 300 - 15c + 10c = 225
We first need to simplify the expression removing parentheses
Our updated term to work with is 300 - 15c + 10c = 225
[SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE]
(-15 + 10)c = -5c
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
-5c + 300 = + 225
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
-5c + 300 - 300 = 225 - 300
[SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE]
-5c = -75
[SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE]
-5c/-5 = -75/-5
c = [B]15[/B]
Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
a = 20 - 15
a = [B]5[/B]

A man's age (a) 10 years ago is 43

A man's age (a) 10 years ago is 43
[U]10 years ago means we subtract 10 from a:[/U]
a - 10
[U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U]
[B]a - 10 = 43[/B]
If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = 53

a mans age (a) ten years ago

a mans age (a) ten years ago
The problem asks for an algebraic expression for age. The phrase [I]ago[/I] means before now, so they were younger. And younger means we [B]subtract[/B] from our current age:
[B]a - 10[/B]

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechan

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechanic works h hours.
Set up the cost function C(h) where h is the number of hours worked:
C(h) = Hourly Rate * h + parts
C(h) = [B]45h + 125[/B]

a number increased by 8 and then tripled

a number increased by 8 and then tripled
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Increased by 8 means we add 8 to x:
x + 8
Then tripled means we multiply the expression x + 8 by 3:
[B]3(x + 8)[/B]

A number y increased by itself

A number y increased by itself
increased by itself means we add the variable y to itself to get our final algebraic expression of:
[B]y + y
[/B]
[I]If[/I] the problem asks you to simplify, we group like terms and get:
[B]2y[/B]

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Writ

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Write two equivalent expressions for the total cost of 9 accessory package. Then find the cost.
Let c be the number of cleats, s be the number of shin guards, and b be the number of balls. We have the following cost function for 9 accessory packages:
[B]9(25c + 14s + 12b)[/B]
But if we multiply through, we get an equivalent expression:
[B]225c + 126s + 108b[/B]

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the monthly charge and use d to represent data
We multiply gigabyte fee by d and add the usage fee:
[B]15d + 30[/B]

a piece of ribbon is y cm long. Ashley cut it into 4 equal pieces to do her 4 sisters hair. write an

a piece of ribbon is y cm long. Ashley cut it into 4 equal pieces to do her 4 sisters hair. write an expression for the amount of ribbon used for each sister
We take y cm and divide it equal among 4 sisters:
[B]y/4[/B]

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of h

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of hours worked. Write the expression that shows how much a plumber charges for a job. Then find how much the plumbers charges for a job lasting 4 hours
[U]Set up the cost function C(h) where h is the number of hours:[/U]
C(h) = Hours worked * hourly rate + house call fee
[B]C(h) = 25h + 45 <-- This is the expression for how much the plumber charges for a job
[/B]
[U]Now determine how much the plumber charges for a job lasting 4 hours[/U]
We want C(4)
C(4) = 25(4) + 45
C(4) = 100 + 45
C(4) = [B]$145[/B]

a printer charges a $30 setup fee plus $2.00 per ticket. Write an algebraic expression for the cost

a printer charges a $30 setup fee plus $2.00 per ticket. Write an algebraic expression for the cost of t tickets. What is the cost of 225 tickets?
Algebraic Expression:
Cost per ticket * t + set up fee
[B]2t + 30[/B]
How much for t = 225?
2(225) + 30
450 + 30
[B]480[/B]

A quarter of a number is greater than or equal to 38

A quarter of a number is greater than or equal to 38.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
A quarter of a number means 1/4, so we have:
x/4
The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38:
[B]x/4 >= 38 <-- This is our algebraic expression
[/B]
If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get:
x >= [B]152[/B]

A rational expression is undefined when what is 0?

A rational expression is undefined when what is 0?
The [B]denominator[/B]. Because division by zero is undefined.

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area o

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area of the rectangle in terms of x.
Area of a rectangle (A) with length(l) and width (w) is expressed as follows:
A = lw
Plugging in our values given above, we have:
[B]A = (x - 7)(x + 5)[/B]

A restaurant is going to raise all their prices by 5%. If the current price of an item is p dollars,

A restaurant is going to raise all their prices by 5%. If the current price of an item is p dollars, write an expression for the price after the increase.
5% = 0.05 as a decimal.
New price = Old Price * (1 + decimal increase)
New price = p * (1 + 0.05)
New price = [B]1.05p[/B]

A restaurant is going to raise all their prices by 7%. If the current price of an item is p dollars

A restaurant is going to raise all their prices by 7%. If the current price of an item is p dollars, write an expression for the price after the increase.
A 7% increase on price means we multiply the current price of p by 1.07. So our algebraic expression is:
[B]1.07p[/B]

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplif

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplify an expression including units to find the total number of people that can ride the roller coaster at one time
6 trains * 3 cars per train * 4 people per car = [B]72 people[/B]

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,0

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,000. If x represents the salesperson’s weekly sales, express the total weekly earnings E(x) as a function of x and simplify the expression. Then find E(2,000) and E(7,000) and E(10,000).
15% as a decimal is written as 0.15.
Build our weekly earnings function
E(x) = Commission + Base Salary
E(x) = 0.15(Max(0, x - 5000)) + 300
Now find the sales salary for 2,000, 7,000, and 10,000 in sales
E(2,000) = 0.15(Max(0,2000 - 5000)) + 300
E(2,000) = 0.15(Max(0,-3000)) + 300
E(2,000) = 0.15(0) + 300
[B]E(2,000) = 300
[/B]
E(7,000) = 0.15(Max(0,7000 - 5000)) + 300
E(7,000) = 0.15(Max(0,2000)) + 300
E(7,000) = 0.15(2,000) + 300
E(7,000) = 300 + 300
[B][B]E(7,000) = 600[/B][/B]
E(10,000) = 0.15(Max(0,10000 - 5000)) + 300
E(10,000) = 0.15(Max(0,5000)) + 300
E(10,000) = 0.15(5,000) + 300
E(10,000) = 750+ 300
[B][B]E(10,000) = 1,050[/B][/B]

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?
Take this algebraic expression in pieces:
[LIST]
[*]Let the secret number be n.
[*]Added to means we add 6 to n: n + 6
[*]The total is multiplied by 5: 5(n + 6)
[*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50
[/LIST]
5(n + 6) = 50
To solve this equation for n, we type it in our search engine and we get:
n = [B]4[/B]

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts.
Cost equals quantity times price, so we have the total cost C:
[B]C(s, j) = 15s + 25j[/B]

A soccer team lost 30% of their games and drew 15% and they played 67 games. How many games did they

A soccer team lost 30% of their games and drew 15% and they played 67 games. How many games did they win
If they lost 30% and they drew (tied) 15%, then they won the following:
Wins = 100% - Losses - Drew
Wins = 100% - 30% - 15%
Wins = 55%
So we want 55% of 67. We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=55&den1=67&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get:
[B]36.85 ~ 37 games[/B]

A sports tournament has c teams. Each team has 17 players. Using c, write

A sports tournament has c teams. Each team has 17 players. Using c, write an expression for the total number of players in the tournament.
Total Players = Total Teams * Players Per Team
Total Players =[B] 17c[/B]

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the tota

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the total number of players in the tournament.
Tournament Players = Players per team * Number of Teams
Tournament Players = [B]14d[/B]

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expressio

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights.
The cost in dollars C is found below:
[B]C = 7.50n + 6[/B]

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expressio

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights.
We write this as:
cost per night of camping * n nights + entry fee
[B]7.50n + 6[/B]

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many doctors use brand A aspirin?
We want 3/5 of 2000. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=2000&frac2=3/5&pl=Multiply']type this expression into our search engine[/URL] and we get:
[B]1,200[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
[LIST]
[*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip.
[*]This expression must be less than 12.
[/LIST]
[U]Setup the inequality:[/U]
1.5 + 0.8x < 12
[U]Subtracting 1.5 from each side of the inequality[/U]
0.8x < 10.5
[U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U]
[B]x < 13.125[/B]

A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair conditio

A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying x excellent-condition paperbacks and f fair-condition paperbacks.
Cost = Price * Quantity, so we have:
[B]2.50x + 0.50f[/B]

absolute value of x is less than or equal to 4

absolute value of x is less than or equal to 4
Absolute value of x:
|x|
Set up an inequality where this is less than or equal to 4:
[B]|x| <= 4 [/B] <-- This is our algebraic expression
To solve this, we have the following compound inequality:
-4 < x < 4

add 7 and 2, raise the result to the 6th power, then add what you have to s

add 7 and 2, raise the result to the 6th power, then add what you have to s
Add 7 and 2:
7 + 2
Simplify this, we get:9
Raise the result to the 6th power:
9^6
[URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=9%5E6&pl=Calculate']Simplifying this using our exponent calculator[/URL], we get:
531,441
Now, we add what we have (our result) to s to get our final algebraic expression:
[B]s + 531,441[/B]

add c and b, multiply the result by a, then double what you have

add c and b, multiply the result by a, then double what you have
Take this algebraic expression in pieces:
[LIST]
[*]add c and b: c + b
[*]Multiply the result by a: a(c + b)
[*]Double what you have means take the last step result, and multiply it by 2:
[/LIST]
[B]2a(c + b)[/B]

add c to b, subtract d from the result, then double what you have

add c to b, subtract d from the result, then double what you have
Add c to b:
b + c
Subtract d from the result:
b + c - d
Double what you have means multiply the entire expression by 2:
[B]2(b + c - d)[/B]

Add q and t, subtract s from the result, then multiply by r

Add q and t, subtract s from the result, then multiply by r
Take this algebraic expression in parts:
[LIST]
[*]Add q and t: q + t
[*]Subtract s from the result: q + t - s
[*]Multiply by r means we multiply the entire expression by r:
[/LIST]
[B]r(q + t - s)[/B]

add r and q, divide the result by s, then triple what you have

add r and q, divide the result by s, then triple what you have
Add r and q:
r + q
Divide the result by s. The result above is r + q, so we have:
(r + q)/s
Triple what you have means we multiply the expression above by 3:
[B]3(r + q)/s[/B]

add r and s, add the result to q, then subtract what you have from p

add r and s, add the result to q, then subtract what you have from p
Take this algebraic expression in 3 parts:
[LIST=1]
[*]Add r and s: r + s
[*]Add the result to q: r + s + q
[*]Subtract what we have from p:
[/LIST]
[B]p - (r + s + q)[/B]

add r to 3, triple the result, then divide s by what you have

add r to 3, triple the result, then divide s by what you have
Take this algebraic expression in parts:
[LIST=1]
[*]Add r to 3: 3 + r
[*]Triple the result means multiply the result above by 3: 3(3 + r)
[*]Then divide s by what you have. [B]s/3(3 + r)[/B]
[/LIST]

add s and t, multiply the result by u, then add r to what you have

add s and t, multiply the result by u, then add r to what you have.
Take this algebraic expression in 3 parts:
[LIST=1]
[*]Add s and t: s + t
[*]Multiply the result by u means me multiply (s + t) times u: u(s + t)
[*]Then add r to what you have. [I]what you have means the result in #2.[/I]
[/LIST]
[B]u(s + t) + r[/B]

add s to v, multiply the result by u, then multiply t by what you have

add s to v, multiply the result by u, then multiply t by what you have
Take this algebraic expression in parts:
[LIST]
[*]Add s to v: v + s
[*]Multiply the result by u: u(v + s)
[*]Then multiply t by what you have:
[/LIST]
[B]tu(v + s)[/B]

add u and t divide s by the result then triple what you have

add u and t divide s by the result then triple what you have
Take this algebraic expression in parts:
[LIST]
[*]Add u and t: u + t
[*]Divide s by the result: s/(u + t)
[*]Triple what you have means we you multiply s/(u + t) by 3
[/LIST]
[B]3s/(u + t)[/B]

add w to t, add u to the result, then divide what you have by v

add w to t, add u to the result, then divide what you have by v
Take this algebraic expression in parts:
[LIST]
[*]Add w to t: t + w
[*]Add u to the result: t + w + u
[*]Divide what you have by v:
[/LIST]
([B]t + w + u)/v[/B]

add w to u, triple the result, then add v to what you have

add w to u, triple the result, then add v to what you have
Take this algebraic expression in parts:
[LIST]
[*]add w to u: w + u
[*]triple the result means we multiply w + u by 3: 3(w + u)
[*]Then add v to what you have
[/LIST]
[B]3(w + u) + v[/B]

Alan is y years old. Beth is 3 years old than Alan.Write an expression for how old Beth is?

Alan is y years old. Beth is 3 years old than Alan.Write an expression for how old Beth is?
The word [I]older[/I] means we add 3 to Alan's age of y. So Beth's age is:
[B]y + 3[/B]

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows th

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows the number of caramels Alec has left.
Alec starts with c caramels. His sister took 85. The word [I]took[/I] means subtract, so we have:
[B]c - 85[/B]

algebraic expression for the sum of x and double the value of y

algebraic expression for the sum of x and double the value of y
Double the value of y means we multiply y by 2:
2y
The sum of x and 2y means we add 2y to x:
[B]x + 2y[/B]

Algebraic Expressions

Free Algebraic Expressions Calculator - This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times)
Also known as Mathematical phrases

algexpress: letthefirstnumberequalx.thesecondnumberis3morethantwicethefirstnumber.expressthesecondnu

Let the first number equal x. The second number is 3 more than twice the first number. Express the second number in terms of the first number x.
[LIST]
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]3 more than means we add 3
[/LIST]
So we have the following algebraic expression:
[B]y = 2x + 3[/B]

All real numbers that are less than equal to -1 or greater than 5

We have two expressions here, so we need a union since we have the word [U]or[/U].
First, All real numbers less than or equal to -1 is x <= -1.
All real numbers greater than 5 is x > 5
So we have x <= -1 U x > 5
[MEDIA=youtube]boOueZTCSuU[/MEDIA]

Alvin planted t fewer trees than Danielle. Danielle planted 56 trees. Write an expression that shows

Alvin planted t fewer trees than Danielle. Danielle planted 56 trees. Write an expression that shows how many trees Alvin planted.
The word [I]fewer[/I] means we subtract, so we have Alvin's tree planting of:
[B]56 - t[/B]

Alyssa has $952 and is spending $27 each week (w) for math tutoring write an algebraic expression to

Alyssa has $952 and is spending $27 each week (w) for math tutoring write an algebraic expression to model the situation
Alyssa's balance is found by using this expression:
[B]952 - 27w[/B]

Amount you spend if you buy a shirt for $20 and jeans for j dollars

Amount you spend if you buy a shirt for $20 and jeans for j dollars
We want an algebraic expression for our total spend. We add the $20 for a shirt plus j for the jeans:
[B]20 + j[/B]

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total number of cards Amy has.
[B]52n[/B]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 18

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes?
Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m):
[B]A(m) = 38,800 - 1800m[/B]

Ana's height is strictly between 63 and 66 inches. Write a symbolic inequality to represent this sce

Ana's height is strictly between 63 and 66 inches. Write a symbolic inequality to represent this scenario. let h be height
[B]63 < h < 66
[/B]
You can also type [I][URL='https://www.mathcelebrity.com/algexpress.php?num=between63and66&pl=Write+Expression']between 63 and 66[/URL][/I] in our search engine.

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
[LIST]
[*]Start with n
[*]Add 20 to it: n + 20
[*]Double it means we multiply the expression by 2: 2(n + 20)
[*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53
[/LIST]
2(n + 20) = 53
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]6.5[/B]

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members?
We're looking for total audience members where [I]20% of what equals 360[/I]?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=360&pct1=20&pcheck=2&pct2=+70&den1=+80&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Type this expression into our search engine[/URL] and we get:
Audience = [B]1,800[/B]

At a recent motorcycle rally, the number of men exceeded the number of women by 247. If x represents

At a recent motorcycle rally, the number of men exceeded the number of women by 247. If x represents the number of women, write an expression for the number of men.
[B]m = x + 247[/B]

At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 per

At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which expression represents how much she will receive in commission from the sale?
Since 18 percent = 0.18, we have:
Commission = Sales * Commission Percent
Commission = 569 * 0.18
Commission = [B]$102.42[/B]

At Billy’s Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower s

At Billy’s Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower seeds, $1.50, and cleats $85.00. Write an expression if you bought b bats, s sunflower seeds, and c cleats.
Since amount = cost * quantity, we have a cost of:
[B]45b + 1.50s + 85c[/B]

b to the fifth power decreased by 7

b to the fifth power decreased by 7
Take this algebraic expression in steps:
[LIST]
[*]b to the fifth power: b^5
[*]Decreased by 7 means we subtract 7 from b^5: [B]b^5 - 7[/B]
[/LIST]

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for the total number of books.
Total Books = Bookcases * shelves per bookcase * books per shelf
Total Books = 1 * 4 * k
Total Books = [B]4k[/B]

Boolean Algebra Multiplication

Free Boolean Algebra Multiplication Calculator - Determines the product of two expressions using boolean algebra.

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the t

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water?
This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have:
6m + 16 >= 58 <-- This is our algebraic expression/inequality.
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get:
[B]m >= 7[/B]

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j )

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j )
Build an algebraic expression:
[B]c = j/2 - 5[/B] <-- Half means we divide by 2 and [I]younger[/I] means we subtract

Concert tickets cost $14.95 each. Which expression represents the total cost of 25 tickets?

Concert tickets cost $14.95 each. Which expression represents the total cost of 25 tickets?
Calculate Total Cost:
Total Cost = Cost Per Ticket * Number of Tickets
Total Cost = $14.95 * 25
Total Cost = [B]$373.75[/B]

d is h decreased by 301

d is h decreased by 301
h decreased by 301 means we subtract 301 from h
h - 301
The phrase [I]is[/I] means equal to, so we set d equal to this expression:
[B]d = h - 301[/B]

Dale has a bookcase with d shelves. There are 14 books on each shelf. Using d, write an expression f

Dale has a bookcase with d shelves. There are 14 books on each shelf. Using d, write an expression for the total number of books.
We multiply the number of shelves by the number of books per shelf.
[B]14d[/B]

Difference between 23 and y is 12

Difference between 23 and y
23 - y
Is, means equal to, so we set 23 - y equal to 12
[B]23 - y = 12
[/B]
If you need to solve this algebraic expression, use our [URL='http://www.mathcelebrity.com/1unk.php?num=23-y%3D12&pl=Solve']equation calculator[/URL]:
[B]y = 11[/B]

divide 8 by t, raise the result to the 7th power

divide 8 by t, raise the result to the 7th power.
We take this algebraic expression in two parts:
1. Divide 8 by t
8/t
2. Raise the result to the 7th power. (This means we use an exponent of 7)
[B](8/t)^7[/B]

Divide a by b, double the result, then multiply c by what you have

Divide a by b, double the result, then multiply c by what you have
Take this algebraic expression in parts:
[LIST]
[*]Divide a by b: a/b
[*]Double the result means multiply by 2: 2a/b
[*]Then multiply c by what you have:
[/LIST]
[B]2ac/b[/B]

divide a by c, triple the result, then subtract what you have from b

divide a by c, triple the result, then subtract what you have from b
Let's take this algebraic expression in parts:
[LIST=1]
[*]Divide a by c: a/c
[*]Triple the result. This means we multiply a/c by 3: 3a/c
[*]Then subtract what you have (the result) from b: b - 3a/c
[/LIST]
[B]b - 3a/c[/B]

divide b by a, subtract the result from c, then add what you have to d

divide b by a, subtract the result from c, then add what you have to d
Take this algebraic expression in 3 parts:
[U]1) Divide b by a:[/U]
b/a
[U]2) Subtract the result from c:[/U]
c - b/a
[U]3) Then add what you have to d:[/U]
[B]c - b/a + d[/B]

Divide the difference of 4 and r by 10

Divide the difference of 4 and r by 10
The difference of 4 and r, mean we subtract r from 4:
4 - r
Now we divide this expression by 10:
[B](4 - r)/10 [/B]

divide the difference of q and s by the sum of p and r

divide the difference of q and s by the sum of p and r
Take this algebraic expression in pieces:
[LIST]
[*]The difference of q and s: q - s
[*]The sum of p and r: p + r
[*]The word [I]divide[/I] means we divide q - s by p + r
[/LIST]
[B](q - s)/(p + r)[/B]

Divide the sum x and y by the difference of subtracting a from b

Divide the sum x and y by the difference of subtracting a from b
The sum x and y is written as:
x + y
The difference of subtracting a from b is written as:
b - a
We divide and get the algebraic expression:
[B](x + y)/(b - a)[/B]

Divide v by the sum of 4 and w

Divide v by the sum of 4 and w
The sum of 4 and w means we add w to 4:
4 + w
Next, we divide v by this sum to get our final algebraic expression:
[B]v/(4 + w)[/B]

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on each of her nature hikes. Write an expression to represent the number of rocks Divya has after she collects rocks on n nature hikes.
For each hike, we have:
[LIST=1]
[*]Start with 70 rocks
[*]She donates half which is 35, which means she's left with 35
[/LIST]
Since each nature hike gives her 3 more rocks, and she goes on n nature hikes, we have the following algebraic expression:
[B]3n + 35[/B]

double the quotient of 4 and 7

double the quotient of 4 and 7
The quotient fo 4 and 7:
4/7
Double means multiply by this expression by 2:
[B]2(4/7)[/B]
If you need to evaluate and simplify this, it's:
[B]8/7[/B]

Dwayne has 9 peppermints. Mary has p fewer peppermints than Dwayne. Choose the expression that shows

Dwayne has 9 peppermints. Mary has p fewer peppermints than Dwayne. Choose the expression that shows how many peppermints Mary has.
The phrase [I]fewer than[/I] means we subtract:
[B]9 - p[/B]

Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to transl

Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translate the above statements into algebraic equation.
Our algebraic expression is:
[B]0.25x = 2
[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%3D2&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]8[/B]

Evaluate the expression (8C3) (7C6)

Evaluate the expression (8C3) (7C6)
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']8C3[/URL] = 56
[URL='https://www.mathcelebrity.com/permutation.php?num=7&den=6&pl=Combinations']7C6[/URL] = 7
(8C3) (7C6) = 56 * 7
(8C3) (7C6) = [B]392[/B]

Evan scored 34 points in a basketball game. 21 of the points were from 3-point shots and the rest we

Evan scored 34 points in a basketball game. 21 of the points were from 3-point shots and the rest were free-throws. What expression shows the points scored from free-throws?
Calculate the points from free throws (f):
f = 34 - 21
f = [B]13[/B]

Expand Master and Build Polynomial Equations

Free Expand Master and Build Polynomial Equations Calculator - This calculator is the __ultimate__ expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)^{x}

* Polynomial Expansions c(d + e + f)^{x}

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)

* Polynomial Expansions c(d + e + f)

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E.

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E.
We find the range of this interval:
Range = Upper Bound - Lower Bound
Range = 0.479 - 0.039
Range = 0.44
Each piece on opposite sides of p gets:
0.44/2 = 0.22
So our expression becomes
[B]p ± 0.22
[MEDIA=youtube]FGZcvcuWCpE[/MEDIA][/B]

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. S

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. Solve for x.
Let's build this algebraic expression in pieces:
The phrase [I]differs from[/I] means a difference.
x - 3
By less than 2/7 means we use the < sign compared to 2/7
x - 3 < 2/7
Finally, the problem says we involve absolute value. So we write this as:
[B]|x - 3| < 2/7[/B]

Factor the following expression: 4a(9b + 7) - 3(9b + 7)

Factor the following expression: 4a(9b + 7) - 3(9b + 7)
The common factor in each term is (9b + 7). Factor this out and we get:
[B](4a - 3)(9b + 7)
[MEDIA=youtube]0thkumkEie0[/MEDIA][/B]

Factoring and Root Finding

Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

Five times Kim's age plus 13 equals 58. How old is Kim?

Five times Kim's age plus 13 equals 58. How old is Kim?
Let Kim's age be a. We have:
Five times Kim's age:
5a
Plus 13 means we add 13
5a + 13
Equals 58 means we set the expression 5a + 13 equal to 58
5a + 13 = 58 <-- This is our algebraic expression
To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get:
a = [B]9[/B]

Four more then double a number is greater than 2

Four more then double a number is greater than 2
Double a number:
A number implies an arbitrary variable, let's call it "x". Double means multiply this by 2
2x
Four more than this:
2x + 4
Now, we set this expression as an inequality greater than 2
[B]2x + 4 > 2[/B]

Four times the quantity six plus two

six plus two:
6 + 2
Four times the quantity six plus two
[B]4(6 + 2) [/B]<-- This is our algebraic expression
If we need to evaluate this, we have:
4(8)
[B]32[/B]

Functions-Derivatives-Integrals

Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ'(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ'(1)

3) 2^{nd} Derivative ƒ''(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ''(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1

3) 2

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

g equals 232 subtracted from the quantity 377 times g

g equals 232 subtracted from the quantity 377 times g
377 times g:
377g
232 subtracted from 377 times g:
377g - 232
We set the variable g equal to this expression:
[B]g = 377g - 232[/B]

g less than 143 is equal to 39 reduced by w

g less than 143 is equal to 39 reduced by w
g less than 143 means we subtract g from 143
143 - g
39 reduced by w means we subtract w from 39
39 - w
We set these 2 expressions equal to each other:
[B]143 - g = 39 - w[/B]

H minus 6 all cubed

H minus 6 all cubed
H minus 6
h - 6
All cubed means raise the entire expression to the 3rd power
(h - 6)^3

HomeWork Help Please Respond ASAP!!!

The phrase a number means an arbitrary variable, let's call it x.
Three times a number:
3x
And 18 means we add 18
3x + 18
The word is means equal to, so we set 3x + 18 equal to -39
3x + 18 = -39
This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19

How old am I if 400 reduced by 3 times my age is 124?

How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]

How old am I of 400 reduced by 2 times my age is 224

How old am I of 400 reduced by 2 times my age is 224
[LIST=1]
[*]Let my age be a.
[*]2 times my age: 2a
[*]400 reduced by 2 times my age: 400 - 2a
[*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression
[/LIST]
[B]400 - 2a = 224
[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]88[/B]

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]Multiply it by 14 and add 13: 14n + 13
[*]Multiply by 5 and add 283: 5n + 283
[/LIST]
The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2:
14n + 13 = 5n + 283
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]30[/B]

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4 and add 141.
Let the number be n.
We have two expressions:
[LIST=1]
[*]Multiply by 14 and add 21 is written as: 14n + 21
[*]Multiply by 4 and add 141 is written as: 4n + 141
[/LIST]
The phrase [I]get the same expression[/I] means they are equal. So we set (1) and (2) equal to each other and solve for n:
14n + 21 = 4n + 141
[URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B21%3D4n%2B141&pl=Solve']Type this equation into our search engine [/URL]to solve for n and we get:
n = [B]12[/B]

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 s

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 subtract 8.
Let the number be n. We're given two equal expressions:
[LIST=1]
[*]3n + 67
[*]6n - 8
[/LIST]
Set the expressions equal to each other since they give the [B]same answer[/B]:
3n + 67 = 6n - 8
We have an equation. [URL='https://www.mathcelebrity.com/1unk.php?num=3n%2B67%3D6n-8&pl=Solve']Type this equation into our search engine and we get[/URL]:
n = [B]25[/B]

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 a

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 and add 93. What is my number?
Let the number be n. We're given two expressions:
[LIST]
[*]Multiply the number by 7: 7n
[*]add 25: 7n + 25. <-- Expression 1
[*]Multiply by 3: 3n
[*]Add 93: 3n + 93 <-- Expression 2
[*]The phrase [I]get the same answer[/I] means both expression 1 and expression 2 are equal. So we set them equal to each other:
[/LIST]
7n + 25 = 3n + 93
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B25%3D3n%2B93&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]17[/B]

I did 4 more problems than Manuel. If I did p problems, write an expression for hw many problems Man

I did 4 more problems than Manuel. If I did p problems, write an expression for hw many problems Manuel did.
Manuel did 4 less, so we subtract:
[B]p - 4[/B]

If 11 times a number is added to twice the number, the result is 104

If 11 times a number is added to twice the number, the result is 104
Let [I]the number[/I] be an arbitrary variable we call x.
11 times a number:
11x
Twice the number (means we multiply x by 2):
2x
The phrase [I]is added to[/I] means we add 2x to 11x:
11x + 2x
Simplify by grouping like terms:
(11 + 2)x = 13x
The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104:
13x = 104 <-- This is our algebraic expression
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get:
x = [B]8[/B]

If 23.8% of a population is 8,212,000. What is the total population?

If 23.8% of a population is 8,212,000. What is the total population?
This can be written as [I]23.8% of x is 8212000
[/I]
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=23.8&den1=8212000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get:
[B]1,954,456[/B]

If 4 times a number is added to 9, the result is 49

If 4 times a number is added to 9, the result is 49.
[I]A number[/I] means an arbitrary variable, let's call it x.
4 [I]times a number[/I] means we multiply x by 4
4x
[I]Added to[/I] 9 means we add 9 to 4x
4x + 9
[I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49
[B]4x + 9 = 49[/B] <-- This is our algebraic expression
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10

If 44% of a number is 120, find 11% of that number.

If 44% of a number is 120, find 11% of that number.
[URL='https://www.mathcelebrity.com/algexpress.php?num=44%ofanumberis120&pl=Write+Expression']44% of a number is 120[/URL]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.44x%20%3D%20120&pl=Solve']Solving for x, we get 272.72[/URL]
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=11&den1=272.727272&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']11% of this is [/URL][B]30[/B]

If 72 is added to a number it will be 4 times as large as it was originally

If 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]

If a is 4 and b is 6, what is the value of this expression? sqrt(a^2+2b-3)

If a is 4 and b is 6, what is the value of this expression? sqrt(a^2+2b-3)
Plug in our values for a and b:
sqrt(4^2+2(6)-3)
sqrt(16 + 12 - 3)
sqrt(25)
[B]5
[MEDIA=youtube]A3Wh4f57ueo[/MEDIA][/B]

if a number is tripled the result is 60

if a number is tripled the result is 60
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Triple the number means we multiply by 3:
3x
The phrase [I]the result is[/I] means an equation, so we set 3x equal to 60:
[B]3x = 60 <-- This is our algebraic expression
[/B]
If you want to solve this equation, then [URL='https://www.mathcelebrity.com/1unk.php?num=3x%3D60&pl=Solve']you type in 3x = 60 into the search engine[/URL] and get:
x = 20

If from twice a number you subtract four, the difference is twenty

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
Subtract four:
2x - 4
The word [I]is [/I]means equal to. We set 2x - 4 equal to 20 for our algebraic expression:
[B]2x - 4 = 20
[/B]
If the problem asks you to solve for x:
we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-4%3D20&pl=Solve']plug this equation into our calculator [/URL]and get x = [B]12[/B]

If i triple the number then subtract 7 the answer is 2. What is the number

If i triple the number then subtract 7 the answer is 2. What is the number
Let the number be x.
Triple the number:
3x
Subtract 7
3x - 7
The answer is 2 means we set:
[B]3x - 7 = 2[/B]
This is our algebraic expression. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D2&pl=Solve']we type this problem into the search engine[/URL] and get [B]x = 3[/B].

If m% of m is 36, then m is?

If m% of m is 36, then m is?
m% = m/100, so we have:
m/100 * m = 36
m^2/100 = 36
Cross multiply and we get:
m^2 = 3600
We use our [URL='https://www.mathcelebrity.com/radex.php?num=sqrt(3600%2F1)&pl=Simplify+Radical+Expression']radical expressions simplifier[/URL] to get:
m = [B]60
[MEDIA=youtube]vlsIbZz4dx4[/MEDIA][/B]

If sales tax is currently 8.2%, write an algebraic expression representing the amount of sales tax y

If sales tax is currently 8.2%, write an algebraic expression representing the amount of sales tax you would have to pay for an item that costs D dollars.
8.2% is 0.082 as a decimal. So we have:
Sales Tax Paid = [B]0.082D[/B]

If thrice a number is increased by 11,the result is 35. What is the number

If thrice a number is increased by 11,the result is 35. What is the number?
[LIST]
[*]The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
[*]Thrice means multiply by 3, so we have 3x
[*]Increased by 11 means we add 11, so we have 3x + 11
[*]The [I]result is[/I] means an equation, so we set 3x + 11 equal to 35
[/LIST]
3x + 11 = 35 <-- This is our algebraic expression
The problem ask us to solve the algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B11%3D35&pl=Solve']Typing this problem into our search engine[/URL], we get [B]x = 8[/B].

If twice a number is divided by 7, the result is -28

If twice a number is divided by 7, the result is -28.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
Twice x means we multiply x by 2: 2x
Divide this by 7: 2x/7
We set this equal to -28, and we have our algebraic expression:
[B]2x/7 = -28 [/B]

if you add 35 to twice a number, the result is 17. What is the number?

if you add 35 to twice a number, the result is 17. What is the number?
A number is represented by a variable, let's call it "x".
Twice a number means we multiply by 2 --> 2x
Add 35
2x + 35
Now set that entire expression equal to 17
2x + 35 = 17
[URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B35%3D17&pl=Solve']Plug that into the search engine to solve for x[/URL]
[B]x = -9[/B]

if you add 7 to 2x, the result is 17

if you add 7 to 2x, the result is 17
Add 7 to 2x:
2x + 7
The phrase [I]the result is[/I] means an equation, so we set 2x + 7 = 17
[B]2x + 7 = 17 [/B] <-- This is our algebraic expression
Now, if you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B7%3D17&pl=Solve']type in 2x + 7 = 17 into the search engine[/URL], and we get [B]x = 5[/B].

If you have $272, and you spend $17 each day, how long would it be until you had no money left?

If you have $272, and you spend $17 each day, how long would it be until you had no money left?
Let d be the number of days. We have a balance expression of:
272 - 17d
We want to know when the balance is 0, so we set 272 - 17d equal to 0.
272 - 17d = 0
To solve for d, we [URL='http://272 - 17d = 0']type this equation into our search engine[/URL] and we get:
d = [B]16[/B]

If you multiply me by 33 and subtract 20, the result is 46. Who am I?

If you multiply me by 33 and subtract 20, the result is 46. Who am I?
[LIST]
[*]Start with the variable x
[*]Multiply me by 33 = 33x
[*]Subtract 20: 33x - 20
[*]The result is 46, means we set this expression equal to 46: 33x - 20 = 46
[/LIST]
Run this through our [URL='http://www.mathcelebrity.com/1unk.php?num=33x-20%3D46&pl=Solve']equation calculator[/URL], and we get:
[B]x = 2[/B]

In 2016, National Textile installed a new textile machine in one of its factories at a cost of $300,

In 2016, National Textile installed a new textile machine in one of its factories at a cost of $300,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000. (a) Find an expression for the textile machines book value in the t th year of use (0 ≤ t ≤ 10)
We have a straight line depreciation. Book Value is shown on the [URL='http://www.mathcelebrity.com/depsl.php?d=&a=300000&s=10000&n=10&t=3&bv=&pl=Calculate']straight line depreciation calculator[/URL].

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience?
If 80% were adults, this means 100% - 80% = 20% were children.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=20&den1=500&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We type the expression 20% of 500 into our search engine[/URL] and get [B]100 children[/B]

is 6x a monomial?

[B]Yes[/B]. It's an algebraic expression consisting of one term.
The constant is 6, and the variable is x.

Is it correct to word "10% * 50 + 50" as "10% upper 50"?

If we factor your expression, we get:
y > x(10% + 1)
y> 1.1x Since 10% is 0.1
I read it as y > 110% of x

Is it correct to word "10% * 50 + 50" as "10% upper 50"?

Yes, that's a way. However, in my case, I need to interpret the expression with the "upper" definition. Could you help me?

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible nu

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible numbers of additional minutes she will run?
Set up our inequality. If she ran 22 minutes, we need to find an expression to find out the remaining minutes
x + 22 < 36
Subtract 22 from each side:
x < 14
Remember, she cannot run negative minutes, so our lower bound is 0, so we have:
[B]0 < x < 14
[/B]

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amou

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amount E. Write an expression to show how much he earned per day in a month. Suppose he is working for 20 days per month.
[LIST=1]
[*]Each day, Jay earns a profit of S - E.
[*]For one month (30 days), he earns 30(S - E)
[*]For 20 working days in a month, he earns 20(S - E)
[/LIST]

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?
Set up a proportion of trees planted to hours where t is the number of trees planted in 10 hours.
10/4 = t/10
[URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=t&den1=4&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']Type this expression into the search engine[/URL] and we get [B]t = 25[/B].
This means Jeremy can plant 25 trees in 10 hours.

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday a

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday and Saturday. Write an expression to represent how much joe earned.
Earnings = Hourly Rate * hours worked, so we have:
[LIST]
[*]Wednesday: 9x
[*]Friday: 9x
[*]Tuesday: 9(8) = 72
[*]Saturday: 9(8) = 72
[/LIST]
Joe's total earnings come from adding up all 4 days:
9x + 9x + 72 + 72
Combine like terms:
(9 + 9)x + (72 + 72)
[B]18x + 144[/B]

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total number of marbles John now has.
More means we add:
[B]x + 6[/B]

Jordan practices his trombone for 45 minutes each day. Write an expression for the number of minutes

Jordan practices his trombone for 45 minutes each day. Write an expression for the number of minutes Jordan practices she practices the trombone in d days.
Let m = the number of minutes practiced. We ave:
[B]m = 45d[/B]

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51
Let JP's age be j. Let Reyna's age be r. We're given two expressions:
[LIST=1]
[*]w = 2r
[*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I]
[/LIST]
We substitute (1) into (2) for w to get the inequality:
r + 2r <= 51
To solve this inequality, we type it in our search engine and we get:
[B]r <= 17[/B]

k equals the sum of h and 23

The sum of h and 23 means we add:
h + 23
k equals means we set our expression above equal to k
h + 23 = k

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

Kimi has 62 red peppers and g green peppers. Choose the expression that shows how many peppers Kimi

Kimi has 62 red peppers and g green peppers. Choose the expression that shows how many peppers Kimi has.
We add to get the total peppers:
[B]62 + g[/B]

last week, bill drove 252 miles. This week, he drove m miles. Using m , write an expression for the

last week, bill drove 252 miles. This week, he drove m miles. Using m, write an expression for the total number of miles he drove in the two weeks
We add the distance driven:
[B]252 + m[/B]

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the total number of miles he biked.
We add both years to get our algebraic expression of miles biked:
[B]m + 524[/B]

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for th

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for the total number of miles she biked.
[U]Calculate Total miles biked[/U]
Total miles biked = Last Year + This year
Total miles biked = [B]m + 390[/B]

Lauren's savings increased by 12 and is now 31

Lauren's savings increased by 12 and is now 31
[LIST]
[*]Let Lauren's savings be s.
[*]The phrase increased by means we add.
[*]The phrase [I]is now[/I] means an equation.
[*]We have an algebraic expression of:
[/LIST]
[B]s + 12 = 31
[/B]
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B12%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]19[/B]

Leonard earned $100 from a bonus plus $15 per day (d) at his job this week. Which of the following e

Leonard earned $100 from a bonus plus $15 per day (d) at his job this week. Which of the following expressions best represents Leonards income for the week?
We set up an income function I(d), were d is the number of days Leonard works:
[B]I(d) = 15d + 100
[/B]
Each day, Leonard earns $15. Then we add on the $100 bonus

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside,

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Linda is taking a combined total of 18 credit hours at the two schools. Suppose that she is taking w credit hours at Westside. Write an expression for the combined total dollar amount she paid for her class fees.
Let p be the number of credit hours at Pinewood. We have two equations:
[LIST]
[*]98w for Westside
[*]115p at Pinewood
[*]w + p = 18
[*]Total fees: [B]98w + 115p[/B]
[/LIST]

Logarithms

Free Logarithms Calculator - Using the formula Log a_{b} = e, this calculates the 3 pieces of a logarithm equation:

1) Base (b)

2) Exponent

3) Log Result

In addition, it converts

* Expand logarithmic expressions

1) Base (b)

2) Exponent

3) Log Result

In addition, it converts

* Expand logarithmic expressions

Logarithms and Natural Logarithms and Eulers Constant (e)

Free Logarithms and Natural Logarithms and Eulers Constant (e) Calculator - This calculator does the following:

* Takes the Natural Log base e of a number x Ln(x) → log_{e}x

* Raises e to a power of y, e^{y}

* Performs the change of base rule on log_{b}(x)

* Solves equations in the form b^{cx} = d where b, c, and d are constants and x is any variable a-z

* Solves equations in the form ce^{dx}=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z

* Exponential form to logarithmic form for expressions such as 5^{3} = 125 to logarithmic form

* Logarithmic form to exponential form for expressions such as Log_{5}125 = 3

* Takes the Natural Log base e of a number x Ln(x) → log

* Raises e to a power of y, e

* Performs the change of base rule on log

* Solves equations in the form b

* Solves equations in the form ce

* Exponential form to logarithmic form for expressions such as 5

* Logarithmic form to exponential form for expressions such as Log

M decreased by the sum of 13 and the number P is less than 12

M decreased by the sum of 13 and the number P is less than 12
The sum of 13 and the number P
13 + P
M decreased by the sum of 13 and the number P
M - (13 + P)
Less than 12 means we set this entire expression less than 12 as an inequality
[B]M - (13 + P) < 12[/B]

M is halved, then 7 is added

M is halved, then 7 is added
Take this algebraic expression in parts:
[LIST]
[*]M is halved. This means we divide M by 2: M/2
[*]Then 7 is added. We add 7 to M/2
[/LIST]
[B]M/2 + 7[/B]

mcubemultipliedbyntothefourthpower

mcubemultipliedbyntothefourthpower
m cubed means we raise m to the 3rd power:
m^3
n to the fourth power:
n^4
Multiply both expressions together:
[B]m^3n^4[/B]

Multiply 0 by 3 and add 4

Multiply 0 by 3 and add 4
multiply 0 by 3:
0 * 3
Then add 4:
[B]0 * 3 + 4 <--- [/B][I]This is our algebraic expression.[/I]
If we want to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=0%2A3%2B4&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
[B]4[/B]

multiply 3 by the difference of u and t

multiply 3 by the difference of u and t
Take this algebraic expression in parts:
The difference of u and t means we subtract t from u
u - t
Multiply this difference by 3:
[B]3(u - t)[/B]

multiply k by 5.8, and then subtract 3.09 from the product

multiply k by 5.8, and then subtract 3.09 from the product
Take this algebraic expression in pieces:
[U]Multiply k by 5.8:[/U]
5.8k
[U]Then subtract 3.09 from the product[/U]
[B]5.8k - 3.09[/B]

multiply m by 5, double the result, then multiply 10 by what you have

multiply m by 5, double the result, then multiply 10 by what you have
Take this algebraic expression in parts:
[LIST]
[*]Multiply m by 5: 5m
[*]double the result means multiply 5m by 2: 2(5m) = 10m
[*]Multiply 10 by what you have means multiply 10 by the result of 10m above:
[/LIST]
10(10m) = [B]100m[/B]

multiply r by t, add the result to u, then multiply what you have by s

multiply r by t, add the result to u, then multiply what you have by s
Take this algebraic expression in parts:
[LIST=1]
[*]Multiply r by t: rt
[*]Add the result to u means we add rt to u: u + r
[*]Multiply what you have by s. This means we take the result in #2, u + r, and multiply it by s:
[/LIST]
[B]s(u + r)[/B]

multiply t by u, add the to v, then triple what you have

multiply t by u, add the to v, then triple what you have
Multiply t by u:
tu
Add this to v:
v + tu
Then triple what you have - This means we multiply the expression above by 3:
[B]3(v + tu)[/B]

Multiply the difference of 3 and q by p

Multiply the difference of 3 and q by p.
Take this algebraic expression in pieces:
[B][U]Step 1: The difference of 3 and q[/U][/B]
The word [I]difference[/I] means we subtract the variable q from 3
3 - q
[B][U]Step 2: Multiply the expression 3 - q by p:[/U]
p(3 - q)[/B]

multiply u by s, multiply the result by v, then multiply t

multiply u by s, multiply the result by v, then multiply t
Take this algebraic expression in parts:
[LIST]
[*]Multiply u by s: us
[*]Multiply the result by v: usv
[*]Then multiply by t: [B]usvt[/B]
[/LIST]

Multiplying a number by 6 is equal to the number increased by 9

Multiplying a number by 6 is equal to the number increased by 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Multiply it by 6 --> 6x
We set this equal to the same number increased by 9. Increased by means we add:
[B]6x = x + 9 <-- This is our algebraic expression
[/B]
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3Dx%2B9&pl=Solve']type it into the search engine [/URL]and get x = 1.8.

n increased by the difference between 10 times n and 9

n increased by the difference between 10 times n and 9
Take this algebraic expression in pieces:
[LIST]
[*]10 times n: 10n
[*]The difference between 10 times n and 9: 10n - 9
[*]n increased by the difference...: [B]n + (10n - 9)[/B]
[/LIST]

n is equal to 135 less than the quantity 61 times n

n is equal to 135 less than the quantity 61 times n
61 times n:
61n
135 less than the quantity 61 times n
61n - 135
We set n equal to this expression:
[B]n = 61n - 135[/B]

n is equal to the product of 7 and the sum of m and 6

n is equal to the product of 7 and the sum of m and 6
The sum of m and 6:
m + 6
The product of 7 and this sum:
7(m + 6)
We set this expression equal to n:
[B]7(m + 6) = n[/B]

N reduced by 2 is the same as Z increased by 7

N reduced by 2 is the same as Z increased by 7
[LIST]
[*]N reduced by 2 means subtract --> n - 2
[*]z increased by 7 means add --> z + 7
[*][I]Is the same as[/I] means equal to, so we set these expressions equal to each other
[*][B]n - 2 = z + 7[/B]
[/LIST]

n subtract m, multiply by c, then add w

n subtract m, multiply by c, then add w
Take this algebraic expression in pieces:
[LIST]
[*]n subtract m: n - m
[*]multiply by c: c(n - m)
[*]Then add w: [B]c(n - m) + w[/B]
[/LIST]

Need help on this question

Consider the recurrence relation T(n) =2
if n = 1, T(n−1) + 4n−2
if n > 1
(i) Derive the closed form expression f(n) for this recurrence relation.
(ii) Prove that T(n) = f(n),∀n ∈N

Nine less than the product of 2 and y is not less than 15

The product of 2 and y means we multiply
2y
Nine less than that product means we subtract 9
2y - 9
Finally, the entire expression is not less than 15, which means 15 or more. We use greater than or equal to
[B]2y - 9 >= 15
[/B]
If you want to solve this inequality and write the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=2y-9%3E%3D15&pl=Solve']our calculator[/URL].

Nine less than twelve

less than means we subtract 9 from 12:
[B]12 - 9[/B] <-- This is our algebraic expression
IF we want to evaluate this, it's:
12- 9 = [B]3[/B]

nine times x is twice the sum of x and five

nine times x is twice the sum of x and five
Take this algebraic expression in 4 pieces:
[U]Step 1: nine time x:[/U]
9x
[U]Step 2: The sum of x and five means we add 5 to x:[/U]
x + 5
[U]Step 3: The word [I]twice[/I] means we multiply the sum x + 5 by 2:[/U]
2(x + 5)
[U]Step 4: The word [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) to get our final algebraic expression of:[/U]
[B]9x = 2(x + 5)[/B]

One fifth of the square of a number

One fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The square of a number means we raise it to the power of 2. So we have x^2
[*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below:
[/LIST]
[B]x^2/5[/B]

One-fourth the sum of m and p

One-fourth the sum of m and p
Take this algebraic expression in parts:
[LIST]
[*]The sum of m and p means we add p to m: m + p
[*]1/4 of the sum mean we divide m + p by 4
[/LIST]
[B](m + p)/4[/B]

One-half a number is fifty

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
One-half a number means we divide x by2:
x/2
The word [I]is[/I] means equal to. We set x/2 equal to 50 for our algebraic expression
[B]x/2 = 50
[/B]
If the problem asks us to solve for x, we cross multiply:
x = 2 * 50
x = [B]100[/B]

Order of Operations

Free Order of Operations Calculator - Evaluates an expression using the order of operations, or PEMDAS or PEDMAS or BEDMAS or BODMAS

p decreased by 65 is the same as the total of f and 194

p decreased by 65 is the same as the total of f and 194
p decreased by 65
p - 65
The total of f and 194
f + 194
The phrase [I]is the same as[/I] means equal to, so we set the expressions above equal to each other
[B]p - 65 = f + 194[/B]

p more than the square of q

p more than the square of q
Take this algebraic expression in parts:
Step 1: Square of q means raise q to the 2nd power:
q^2
Step 2: The phrase [I]more[/I] means we add p to q^2
[B]q^2 + p[/B]

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.
Assumptions:
[LIST]
[*]Let Paul's age be p
[*]Let Marina's age be m
[/LIST]
Our expression is:
[B]p = 1/2m - 7[/B]

Pedro has r red peppers and 44 green peppers. Write an expression that shows how many peppers Pedro

Pedro has r red peppers and 44 green peppers. Write an expression that shows how many peppers Pedro has.
Add them together:
[B]r + 44[/B]

Percent Math

Free Percent Math Calculator - Simplifies expressions involving numbers and percents with respect to addition and subtraction

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equati

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equation with x from the information.
Take this algebraic expression in parts, starting with the unknown number x:
[LIST]
[*]x
[*][I]Double it [/I]means we multiply x by 2: 2x
[*]Add 0.8: 2x + 0.8
[*]The phrase [I]to get an answer of[/I] means an equation. So we set 2x + 0.8 equal to 31
[/LIST]
Build our final algebraic expression:
[B]2x + 0.8 = 31[/B]
[B][/B]
If you have to solve for x, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B0.8%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
x = 15.1

Polynomial

Free Polynomial Calculator - This calculator will take an expression without division signs and combine like terms.

It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.

It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.

Positive numbers less than 4

Update, this has been added to our shortcuts.
You can type any expression in the form, positive numbers less than x where x is any integer.
You can also type positive numbers greater than x where x is any integer.
Same with less than or equal to and greater than or equal to.

product of r plus 7 and 4

product of r plus 7 and 4
r plus 7 means we add 7 to r:
r + 7
The product means we multiply the expression r + a 7 by 4:
[B]4(r + 7)[/B]

Prove 0! = 1

Prove 0! = 1
Let n be a whole number, where n! represents the product of n and all integers below it through 1.
The factorial formula for n is:
n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1
Written in partially expanded form, n! is:
n! = n * (n - 1)!
[U]Substitute n = 1 into this expression:[/U]
n! = n * (n - 1)!
1! = 1 * (1 - 1)!
1! = 1 * (0)!
For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above

Prove 0! = 1

[URL='https://www.mathcelebrity.com/proofs.php?num=prove0%21%3D1&pl=Prove']Prove 0! = 1[/URL]
Let n be a whole number, where n! represents:
The product of n and all integers below it through 1.
The factorial formula for n is
n! = n · (n - 1) · (n - 2) · ... · 3 · 2 · 1
Written in partially expanded form, n! is:
n! = n · (n - 1)!
[SIZE=5][B]Substitute n = 1 into this expression:[/B][/SIZE]
n! = n · (n - 1)!
1! = 1 · (1 - 1)!
1! = 1 · (0)!
For the expression to be true, 0! [U]must[/U] equal 1.
Otherwise, 1! ≠ 1 which contradicts the equation above
[MEDIA=youtube]wDgRgfj1cIs[/MEDIA]

Prove that the difference of two consecutive cubes is never divisible by 3

Take two consecutive integers:
n, n + 1
The difference of their cubes is:
(n + 1)^3 - n^3
n^3 + 3n^2 + 3n + 1 - n^3
Cancel the n^3
3n^2 + 3n + 1
Factor out a 3 from the first 2 terms:
3(n^2 + n) + 1
The first two terms are always divisible by 3 but then the + 1 makes this expression not divisible by 3:
3(n^2 + n) + 1 = 1 (mod 3)
[MEDIA=youtube]hFvJ3epqmyE[/MEDIA]

q increased by the difference between 18 times q and 5

q increased by the difference between 18 times q and 5
Take this algebraic expression in parts.
18 times q:
18q
The difference between 18 times q and 5 means we subtract 5 from 18q:
18q - 5
q increased by the difference between 18 times q and 5 means we add 18q - 5 to q:
q + (18q - 5)
[B]q + 18q - 5[/B]
IF we want to simplify, we group like terms:
[B]19q - 5[/B]

q is equal to 207 subtracted from the quantity 4 times q

q is equal to 207 subtracted from the quantity 4 times q
4 time q
4q
207 subtracted from 4 times q:
4q - 207
Set this equal to q:
[B]4q - 207 = q [/B]<-- This is our algebraic expression
To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get:
[B]q = 69[/B]

Radical Expressions

Free Radical Expressions Calculator - Evaluates and simplifies radical expressions. Simplifying radical expressions.

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c.
This is an algebraic expression, let's take in parts (or chunks).
Raise 9 to the 3rd power. This means we take 9, and raise it to an exponent of 3
9^3
Subtract d from the result, means we subtract d from 9^3
9^3 - d
Now we divide 9^3 - d by c
[B](9^3 - d) / c[/B]

Raise c to the 7th power, divide the result by 4, then triple what you have

Raise c to the 7th power, divide the result by 4, then triple what you have.
Take this algebraic expression in pieces.
Raise c to the 7th power:
c^7
Divide the result by 4, means we divide c^7 by 4
c^7 / 4
Triple what you have means multiply c^7 / 4 by 3
[B]3(c^7 / 4)[/B]

raise f to the 3rd power, then find the quotient of the result and g

raise f to the 3rd power, then find the quotient of the result and g
Take this algebraic expression in two parts:
[LIST=1]
[*]Raise f to the 3rd power means we take f, and write it with an exponent of 3: f^3
[*]Find the quotient of the result and g. We take f^3, and divide it by g
[/LIST]
[B]f^3/g[/B]

Raise f to the 8th power, divide the result by 5, then multiply 10

Raise f to the 8th power, divide the result by 5, then multiply 10
f to the 8th power means we raise f to the power of 8 using an exponent:
f^8
Divide f^8 by 5
(f^8)/5
Now multiply this by 10:
10(f^8)/5
We can simplify this algebraic expression by dividing 10/5 to get 2 on top:
2[B](f^8)[/B]

raise q to the 5th power add the result to p then divide what you have by r

raise q to the 5th power add the result to p then divide what you have by r
Take this algebraic expression in parts:
[LIST]
[*]Raise q to the 5th power: q^5
[*]Add the result to p: p + q^5
[*]Divide what you have by r. This means we take our result above and divide it by r:
[/LIST]
[B](p + q^5)/r[/B]

raise z to the 2nd power, multiply 8 by the result then subtract what you have from 4

raise z to the 2nd power, multiply 8 by the result then subtract what you have from 4
Take this algebraic expression in pieces:
[LIST]
[*]Raise z to the 2nd power: z^2
[*]Multiply by 8: 8z^2
[*]Subtract what you have from 4:
[/LIST]
[B]4 - 8z^2[/B]

ratio of the squares of t and u

ratio of the squares of t and u
Ratio is also known as quotient in algebraic expression problems.
The square of t means we raise t to the power of 2:
t^2
The square of u means we raise u to the power of 2:
u^2
ratio of the squares of t and u means we divide t^2 by u^2:
[B]t^2/u^2[/B]

Rational Exponents - Fractional Indices

Free Rational Exponents - Fractional Indices Calculator - This calculator evaluates and simplifies a rational exponent expression in the form a^{b/c} where a is any integer *or* any variable [a-z] while b and c are integers. Also evaluates the product of rational exponents

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-s

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-shirts were in each package.
T-shirts per package = number of packages / number of t-shirts per package
T-shirts per package = [B]8/t[/B]

Rental canoes cost $30 plus $5 per house of use. Which expression gives the cost of renting a canoe

Rental canoes cost $30 plus $5 per house of use. Which expression gives the cost of renting a canoe for h hours
[B]R = 30 + 5h[/B]

Robert buys 3 pounds of bananas at $0.50 per pound and 3 pounds of apples at $1.00 per pound. Which

Robert buys 3 pounds of bananas at $0.50 per pound and 3 pounds of apples at $1.00 per pound. Which of the following expressions represents the total cost of the fruit he bought (in dollars)?
Total Cost of Fruit = Bananas in pounds * cost per banana pound + Apples in pounds * cost per apple pound
Total Cost of Fruit = 3($0.50) + 3($1.00)
Total Cost of Fruit = $1.50 + $3.00
Total Cost of Fruit = [B]$4.00[/B]

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an item that costs d dollars after tax is added to the purchase.
We need to increase the price by 9.1%. Our expression is:
[B]1.091d[/B]

Seven subtracted from the product of 3 and a number is greater than or equal to -26

Seven subtracted from the product of 3 and a number is greater than or equal to -26
[LIST=1]
[*]A number means an arbitrary variable, let's call it x.
[*]The product of 3 and a number is written as 3x
[*]Seven subtracted from 3x is written as 3x - 7
[*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B]
[/LIST]

Simplest Exponent Form

Free Simplest Exponent Form Calculator - This expresses repeating algebraic expressions such as 3*a*a*a*b*b into simplest exponent form.

Simplify sin(x) * cos(x) * tan(x) * csc(x) * sec(x) * cot(x)

We know the following:
[LIST]
[*]csc(x) = 1/sin(x)
[*]sec(x) = 1/cos(x)
[*]cot(x) = 1/tan(x)
[/LIST]
We can rewrite our original expression as:
sin(x) * cos(x) * tan(x)/sin(x) * cos(x) * tan(x)
Everything cancels and we are left with [B]1[/B]
[MEDIA=youtube]MsL-Ni4Hen4[/MEDIA]

Simplify sin^2(x)/(1 - sin^2(x))

We know from the pythagorean theorem:
[SIZE=5][B]sin^2(x) + cos^2(x) = 1[/B]
[B]Subtract sin^2(x) from each side and we get:[/B]
[B][B]cos^2(x) = 1 - [B]sin^2(x)[/B][/B][/B]
[B][B][B]We can rewrite our original expression as:[/B][/B][/B]
[B][B][B]sin^2(x)/cos^2(x)[/B][/B][/B]
[/SIZE]
[B][B][B][SIZE=5]But this expression [/SIZE][SIZE=4]equals[/SIZE][SIZE=5] tan^2(x)[/SIZE][/B][/B][/B]
[MEDIA=youtube]zqYg0VRq5Ak[/MEDIA]

Six less two

less means subtract:
[B]6 - 2[/B] <-- This is our algebraic expression
If we need to evaluate we have:
6 - 2 = [B]4[/B]

Sixteen subtracted from five times a number equals the number plus four

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
5 times a number
5x
Sixteen subtracted from five times a number
5x - 16
the number plus 4:
x + 4
Equals means we set 5x - 16 equals to x + 4 for our algebraic expression:
[B]5x - 16 = x + 4[/B]
[B][/B]
If you have to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-16%3Dx%2B4&pl=Solve']type this expression into our math solver[/URL] and we get:
x = [B]5[/B]

Square Roots and Exponents

Free Square Roots and Exponents Calculator - Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Squaring a number equals 5 times that number

Squaring a number equals 5 times that number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Squaring this number:
x^2
5 times this number means we multiply by 5:
5x
The phrase [I]equals[/I] means we set both expressions equal to each other:
[B]x^2 = 5x [/B] <-- This is our algebraic expression
If you want to solve for x, then we subtract 5x from each side:
x^2 - 5x = 5x - 5x
Cancel the 5x on the right side, leaving us with 0:
x^2 - 5x = 0
Factor out x:
x(x - 5)
So we get x = 0 or [B]x = 5[/B]

Start with x , subtract 6, then times by 3.

Start with x , subtract 6, then times by 3.
We start with x:
x
Subtract 6:
x - 6
The phrase [I]times by[/I] means we multiply (x - 6) by 3
[B]3(x - 6) [/B] <-- This is our algebraic expression
If the problem asks you to multiply through, then you'd have:
3x - 18

Subtract 4 from the sum of 2x and 5y

Subtract 4 from the sum of 2x and 5y.
The sum of 2x and 5y means we add both terms:
2x + 5y
Subtract 4 from this sum to get our algebraic expression:
[B](2x + 5y) - 4[/B]

subtract 5 from the sum of 3x and 8y

subtract 5 from the sum of 3x and 8y
Take this algebraic expression in parts:
[U]The sum of 3x and 8y means we add 8y to 3x:[/U]
3x + 8y
[U]Subtract 5 from this sum above:[/U]
[B]3x + 8y - 5[/B]

subtract w from u, triple the result, then multiply v by what you have

subtract w from u, triple the result, then multiply v by what you have
Take this algebraic expression in 3 parts:
[U]1) subtract w from u:[/U]
u - w
[U]2) Triple the result means we multiply u - w by 3:[/U]
3(u - w)
[U]3) Multiply v by what you have. [I]What you have[/I] means the result from step 2:[/U]
[B]3v(u - w)[/B]

subtract w from v, add the result to u, then triple what you have

subtract w from v, add the result to u, then triple what you have
Take this algebraic expression in parts:
[LIST=1]
[*]Subtract w from v: v - w
[*]Add the result to u (the result is #1): u + v - w
[*]Triple what you have. This means multiply the result in #2 by 3:
[/LIST]
[B]3(u + v - w)[/B]

sum of 5 times h and twice g is equal to 23

sum of 5 times h and twice g is equal to 23
Take this [U]algebraic expressions[/U] problem in pieces.
Step 1: 5 times h:
5h
Step 2: Twice g means we multiply g by 2:
2g
Step 3: sum of 5 times h and twice g means we add 2g to 5h
5h + 2g
Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23:
[B]5h + 2g = 23[/B]

sum of a number and 7 is subtracted from 15 the result is 6.

Sum of a number and 7 is subtracted from 15 the result is 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take this expression in pieces. Sum of a number and 7
x + 7
Subtracted from 15
15 - (x + 7)
The result is means an equation, so we set this expression above equal to 6
[B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B]
If the problem asks you to solve for x, we Group like terms
15 - x - 7 = 6
8 - x = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]

Sum of a number and it's reciprocal is 6. What is the number?

Sum of a number and it's reciprocal is 6. What is the number?
Let the number be n.
The reciprocal is 1/n.
The word [I]is[/I] means an equation, so we set n + 1/n equal to 6
n + 1/n = 6
Multiply each side by n to remove the fraction:
n^2 + 1 = 6n
Subtract 6n from each side:
[B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression
If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a c

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Let t be the number of hours for math tutoring and w be the number of hours for waitressing. We're given:
[LIST=1]
[*]t + w = 104
[*]14t + 13w = D <-- Combined total dollar amount
[/LIST]

Ten subtracted from the product of 9 and a number is less than −24

Ten subtracted from the product of 9 and a number is less than −24.
A number means an arbitrary variable, let's call it x
x
The product of 9 and a number:
9x
Ten subtracted from that
9x - 10
Finally, is less than means we set our entire expression less than -24
[B]9x - 10 < -24[/B]

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in Asia is Y square miles, express the area of a desert in Africa as an algebraic expression in Y.
[B]Africa Area = 12Y[/B]

The average of 16 and x is 21. Find x.

The average of 16 and x is 21. Find x.
The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have:
(16 + x)/2 = 21
Cross multiply:
16 + x = 21*2
16 + x = 42
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B].
Check our work by restating our answer:
The average of 16 and 26 is 21. TRUE.

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
Take this in algebraic expression in parts:
[U]Term 1[/U]
[LIST]
[*]The square of y means we raise y to the 2nd power: y^2
[*]5 times the square of y: 5y^2
[/LIST]
[U]Term 2[/U]
[LIST]
[*]2 times y: 2y
[*]The square of 2 times y: (2y)^2 = 4y^2
[*]7 divide by the square of 2 times y: 7/4y^2
[/LIST]
[U]The difference of these terms is written as Term 1 minus Term 2:[/U]
[LIST]
[*]5y^2/4y^2
[/LIST]
[U]The cube of the difference means we raise the difference to the power of 3:[/U]
[B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4

the cube of the difference of 5 times x and 4
Take this algebraic expression in pieces:
5 times x:
5x
The difference of 5x and 4 means we subtract 4 from 5x:
5x - 4
We want to cube this difference, which means we raise the difference to the power of 3.
[B](5x - 4)^3[/B]

the difference between 7 times a number and 9 less than a number

the difference between 7 times a number and 9 less than a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 times a number means we multiply x by 7
7x
9 less than a number means we subtract 9 from x
x - 9
The difference between the two expressions means we subtract (x - 9) from 7x
7x - (x - 9)
Simplifying this, we have:
7x - x + 9
Grouping like terms, we get:
[B]6x + 9[/B]

The difference between a and b is 10

The difference between a and b is 10.
The problem asks for an algebraic expression. Let's take each piece one by one:
[I]Difference between[/I] means we subtract:
a - b
The phrase [I]is [/I]means an equation, so we set a - b equal to 10
[B]a - b = 10[/B]

The difference in Julies height and 9 is 48 letting j be Julie's height

The difference in Julies height and 9 is 48 letting j be Julie's height
Step 1: If Julie's height is represented with the variable j, then we subtract 9 from j since the phrase [I]difference[/I] means we subtract:
j - 9
Step 2: The word [I]is[/I] means an equation, so we set j - 9 equal to 48 for our final algebraic expression:
[B]j - 9 = 48[/B]

The difference of 100 and x is 57

The difference of 100 and x means we subtract x from 100:
100 - x
Is means equal to, so we set our expression above equal to 57
[B]100 - x = 57
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=100-x%3D57&pl=Solve']equation calculator[/URL]

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the num

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
We have two expressions:
[U]Expression 1: [I]The difference of a number and 6[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The difference of a number and 6 means we subtract 6 from x:
x - 6
[U]Expression 2: [I]5 times the sum of the number and 2[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 2 means we add 2 to x:
x + 2
5 times the sum means we multiply x + 2 by 5
5(x + 2)
[U]For the last step, we evaluate the expression [I]is the same as[/I][/U]
This means equal to, so we set x - 6 equal to 5(x + 2)
[B]x - 6 = 5(x + 2)[/B]

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown n

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number.
The phrase a number uses the variable w.
3 times w is written as 3w
The difference of 3w and 6 is written as 3w - 6
Set this equal to 7
[B]3w - 6 = 7
[/B]
This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].

The difference of five and five y is the same as eight and two y

The difference of five and five y
5 - 5y
eight and two y
8 + 2y
The phrase [I]is the same as[/I] means equal to. Set 5 - 5y equal to 8 + 2y for our final algebraic expression
[B]5 - 5y = 8 + 2y[/B]
[B][/B]
If the problem asks you to solve for y:
Add 5y to each side:
5 = 8 + 7y
Subtract 8 from each side:
7y = -3
Divide each side by 7:
[B]y= -3/7[/B]

The difference of twice a number and 4 is at least -27

The difference of twice a number and 4 is at least -27.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Twice a number means multiply the number by 2
2x
[I]and 4[/I] means we add 4 to our expression:
2x + 4
[I]Is at least[/I] means an inequality. In this case, it's greater than or equal to:
[B]2x + 4 >= -27
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B4%3E%3D-27&pl=Solve']type it in the search engine[/URL].

The difference of twice a number and 6 is at most 28

The difference of twice a number and 6 is at most 28
This is an algebraic expression. Let's take it in parts:
[LIST=1]
[*]The phrase [I]a number[/I], means an arbitrary variable, let's call it x
[*]Twice this number means we multiply x by 2: 2x
[*][I]The difference of[/I] means subtract, so we subtract 6 to 2x: 2x - 6
[*][I]Is at most [/I]means less than or equal to, so we create an inequality where 2x - 6 is less than or equal to 28, using the <= sign
[/LIST]
[B]2x - 6 <= 28
[/B]
If you wish to solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-6%3C%3D28&pl=Solve']click this link[/URL].

the difference of twice a number and 8 is at most -30

the difference of twice a number and 8 is at most -30.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice this number means we multiply by 2, so we have 2x.
We take the difference of 2x and 8, meaning we subtract 8:
2x - 8
Finally, the phrase [I]at most[/I] means an inequality, also known as less than or equal to:
[B]2x - 8 <= 30 <-- This is our algebraic expression
[/B]
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-8%3C%3D30&pl=Solve']type it into the search engine[/URL] and get x <= 19.

the difference of x and y added to twice the sum of a and b

the difference of x and y added to twice the sum of a and b
Take this algebraic expression in parts:
[LIST]
[*]The difference of x and y: x - y
[*]The sum of a and b: a + b
[*]Twice the sum of a and b means we multiply a + b by 2: 2(a + b)
[*]The phrase [I]added to[/I] means we add:
[/LIST]
[B]x - y + 2(a + b)[/B]

The expression (5x - 2)/(x + 3) is equivalent to which of the following?

The expression (5x - 2)/(x + 3) is equivalent to which of the following?
[LIST]
[*]A) (5 - 2)/3
[*]B) 5 - 2/3
[*]C) 5 - (2/(x + 3))
[*]D) 5 - (17/(x + 3))
[/LIST]
Let's start with an integer x = 2. Plug that into our original expression, and we get:
(5(2) - 2)(2 + 3)
(10 - 2)/5
8/5
So what we do next is, take x = 2, and plug it into answer choices A-D, and see which one results in 8/5
A) 3/3 = 1 <-- Nope
B) Since 5 is 15/3, we have 15/3 - 2/3 = 13/3 which is over 4, so Nope
C) 5 - (2/(2 + 3)) = 5 - (2/5). Since 5 is 25/5, we have 25/5 - 2/5 = 23/5. <-- Nope
D) 5 - (17/(2 + 3)) = 5 - 17/5. Since 5 is 25/5, we have 25/5 - 17/5 = 8/5 <-- YES
Since 8/5 = 8/5, our answer is [B]D) 5 - (17/(x + 3))[/B]

The larger of 2 numbers is 1 more than 3 times the smaller number

The larger of 2 numbers is 1 more than 3 times the smaller number.
Let the larger number be l. Let the smaller number be s. The algebraic expression is:
3 times the smaller number is written as:
3s
1 more than that means we add 1
3s + 1
Our final algebraic expression uses the word [I]is[/I] meaning an equation. So we set l equal to 3s + 1
[B]l = 3s + 1[/B]

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the wi

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the width?
5.8 feet less than 6 times the width is an algebraic expression:
6w - 5.8
We set this equal to the length of 50.6
6w - 5.8 = 50.6
Add 5.8 to each side:
6w - 5.8 + 5.8 = 50.6 + 5.8
Cancel the 5.8 on the left side:
6w = 56.4
Divide each side by 6:
6w/6 = 56.4/6
[URL='http://www.mathcelebrity.com/1unk.php?num=6w-5.8%3D50.6&pl=Solve']Typing this problem into the search engine[/URL], we get [B]w = 9.4[/B].
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The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per

The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per year since. Write an expression that shows the population of Westport at the beginning of 1994 and solve.
1994 - 1980 = 14 years.
Using our [URL='https://www.mathcelebrity.com/population-growth-calculator.php?num=thepopulationofwestportwas43000hassteadilydecreasedby1%for14years&pl=Calculate']population calculator[/URL], we get:
[B]37,356[/B]

the product of 2 less than a number and 7 is 13

the product of 2 less than a number and 7 is 13
Take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Part 2 - 2 less than a number means we subtract 2 from x
x - 2
Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7
7(x - 2)
Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13
[B]7(x - 2) = 13[/B]

the product of 8 and 15 more than a number

the product of 8 and 15 more than a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
15 more than x means we add 15 to x:
x + 15
The product of 8 and 15 more than a number means we multiply 8 by x + 15
[B]8(x + 15)[/B]

The product of 8 and a number k is greater than 4 and no more than 16

This is now a shortcut on our website. Any expressions in this format will run.

the product of a number and 15 is not less than 15

the product of a number and 15 is not less than 15
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
the product of a number and 15 means we multiply x by 15
15x
The phrase [I]not less than[/I] means greater than or equal to. We set 15x greater than prequel to 15
[B]15x >= 15 <-- This is our algebraic expression
[/B]
[U]If the problem asks you to solve for x:[/U]
Divide each side by 15:
15x/15 >= 15/15
[B]x >= 1[/B]

the product of k and 70, minus 15

the product of k and 70, minus 15
Take this algebraic expression in pieces:
The product of k and 70 means we multiply 70 times k
70k
The word [I]minus[/I] means we subtract 15 from 70k
[B]70k - 15[/B]

The product of two consecutive integers is greater than 100

The product of two consecutive integers is greater than 100
Take an integer x.
Next consecutive integer is x + 1
The product of those integers is:
x(x + 1)
This product is greater than 100 which gives us the algebraic expression of:
x(x + 1) > 100
IF we want to solve for x:
x^2 + x > 100
Subtract 100 from each side:
x^2 + x - 100 > 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-100%3E0&pl=All&hintnum=+0']Solve this quadratic:[/URL]

The product of x and 7 is not greater than 21

The product of x and 7 is not greater than 21
The product of x and 7:
7x
Is not greater than means less than or equal to, so we have our algebraic expression:
7x <= 21
If you want to solve this inequality and interval notation, use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=7x%3C%3D21&pl=Show+Interval+Notation']calculator[/URL].
[MEDIA=youtube]pyYaiKSI0ZQ[/MEDIA]

the quotient of 3 and u is equal to 52 divided by u

the quotient of 3 and u is equal to 52 divided by u
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The quotient of 3 and u means we divide 3 by u: 3/u
[*]52 divided by u means we divide 52 by u: 52/u
[*]The phrase [I]is equal to[/I] means an equation, so we set (1) equal to (2)
[/LIST]
[B]3/u = 52/u[/B]

the quotient of 4 more than a number and 7 is 10

the quotient of 4 more than a number and 7 is 10
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 more than a number means we add 4 to x:
x + 4
The quotient of 4 more than a number and 7 means we divide x + 4 by 7
(x + 4)/7
The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10 to get our algebraic expression of:
[B](x + 4)/7 = 10
[/B]
If the problem asks you to solve for x, then we cross multiply:
x + 4 = 10 * 7
x + 4 = 70
Subtract 4 from each side:
x + 4 - 4 = 70 - 4
x = [B]66
[MEDIA=youtube]j-GZLPVKbTM[/MEDIA][/B]

the quotient of d and 182 is the same as w minus 137

The quotient of d and 182 is the same as w minus 137
Take this algebraic expression in 3 parts:
The quotient of d and 182
d/182
w minus 137
w - 137
The phrase [I]is the same as[/I] means we set d/182 equal to w - 137
[B]d/182 = w - 137[/B]

the ratio of 50 and a number added to the quotient of a number and 10

the ratio of 50 and a number added to the quotient of a number and 10
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of 50 and x means we divide by 50 by x
50/x
The quotient of a number and 10 means we have a fraction:
x/10
The phrase [I]added to[/I] means we add 50/x to x/10
[B]50/x + x/10[/B]

the ratio of a number x and 4 added to 2

the ratio of a number x and 4 added to 2
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of this number and 4 means we have a fraction:
x/4
The phrase [I]added to[/I] means we add 2 to x/4
[B]x/4 + 2[/B]

The ratio of men to women working for a company is 5 to 3 . If there are 75 men working for the

The ratio of men to women working for a company is 5 to 3 . If there are 75 men working for the company, what is the total number of employees?
We read this as a proportion, of men to women.
5/3 = 75/w where w is the number of women for 75 men.
Entering this expression into our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=75&propsign=%3D&den1=3&den2=w&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]w = 45[/B].

the reciprocal of the product a and b

the reciprocal of the product a and b
Take this algebraic expression in pieces:
The product a and b means we multiply a times b
ab
The [I]reciprocal[/I] means we take 1 over ab
[B]1/ab[/B]

The square of a number added to its reciprocal

The square of a number added to its reciprocal
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
the square of x mean we raise x to the power of 2. It's written as:
x^2
The reciprocal of x is 1/x
We add these together to get our final algebraic expression:
[B]x^2 + 1/x
[MEDIA=youtube]ZHut58-AoDU[/MEDIA][/B]

The square of the sum of twice a number x and y

The square of the sum of twice a number x and y
Take this in algebraic expression in 3 parts:
[LIST=1]
[*]Twice a number x means we multiply x by 2: 2x
[*]The sum of twice a number x and y means we add y to 2x above: 2x + y
[*]The square of the sum means we raise the sum (2x + y) to the second power below:
[/LIST]
[B](2x + y)^2[/B]

The sum of 2 and w is less than or equal to 27.

The sum of 2 and w is less than or equal to 27.
Take this algebraic expression in parts:
[LIST]
[*]The sum of 2 and w: 2 + w
[*]The phrase [I]less than or equal to[/I] means an inequality, using the <= sign.
[/LIST]
[B]2 + w <= 27[/B]

the sum of 23 and victor age is 59

the sum of 23 and victor age is 59
Let's Victor's age be a.
The sum of 23 and Victor's age (a) mean we add a to 23:
23 + a
The word [I]is[/I] means an equation, so we set 23 + a equal to 59:
[B]23 + a = 59[/B] <-- This is our algebraic expression
Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]a = 36[/B]

the sum of 3 consecutive natural numbers, the first of which is n

the sum of 3 consecutive natural numbers, the first of which is n
Natural numbers are counting numbers, so we the following expression:
n + (n + 1) + (n + 2)
Combine n terms and constants:
(n + n + n) + (1 + 2)
[B]3n + 3
Also expressed as 3(n + 1)[/B]

The sum of 4 and x is multiplied by 5. The result is then taken away from 16

The sum of 4 and x is multiplied by 5. The result is then taken away from 16.
Take this algebraic expression in 3 parts:
[U]Part 1: The sum of 4 and x:[/U]
4 + x
[U]Part 2: Multiplied by 5:[/U]
5(4 + x)
[U]Part 3: The result is then taken away from 16:[/U]
[B]16 - 5(4 + x)[/B]

the sum of 5 and y is less than or equal to -21

the sum of 5 and y is less than or equal to -21
Take this algebraic expression in parts:
The sum of 5 and y means we add y to 5
5 + y
The phrase [I]less than or equal to[/I] -21 means an inequality. We use the <= sign to relate 5 + y to -21
[B]5 + y <= -21[/B]

the sum of 6 and 7, plus 5 times a number, is -12

the sum of 6 and 7, plus 5 times a number, is -12
The sum of 6 and 7 means we add the two numbers:
6 + 7
This evaluates to 13
Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5:
5x
The first two words say [I]the sum[/I], so we add 13 and 5x
13 + 5x
The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12
[B]13 + 5x = -12[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get:
[B]x = -5[/B]

The sum of 9 and victors age is 55

The sum of 9 and victors age is 55
Let v be Victor's age. We have the algebraic expression:
[B]v + 9 = 55
[/B]
If you want to solve or v, use our [URL='http://www.mathcelebrity.com/1unk.php?num=v%2B9%3D55&pl=Solve']equation calculator[/URL].

The sum of a and b divided by their product

The sum of a and b divided by their product
The sum of a and b means we add b to a:
a + b
The product of a and b means we multiply a by b:
ab
To get our final algebraic expression, we divide the sum (a + b) by the product ab:
[B](a + b)/ab[/B]

The sum of a number and 5 divided by 8

The sum of a number and 5 divided by 8.
Let's take this algebraic expression in parts.
Part 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Part 2: The sum of a number and 5 means we add 5 to the number x
x + 5
Part 3: Next, we divide this expression by 8
[B](x + 5)/8[/B]

the sum of a number and itself is 8

A number means an arbitrary variable, let's call it x.
The sum of a number and itself means adding the number to itself
x + x
Simplified, we have 2x
The word is means equal to, so we have an algebraic expression of:
[B]2x= 8
[/B]
IF you need to solve this equation, divide each side by 2
[B]x = 4[/B]

the sum of a number divided by 8 and 3 equals 6

"A Number" means an arbitrary variable, let's call it x.
x divide d by 8 is written as a quotient
x/8
The sum of x/8 and 3 means we add:
x/8 + 3
Finally, equals means we have an equation, so we set our expression above equal to 6
x/8 + 3 = 6

The sum Of a number squared and 14

The sum Of a number squared and 14.
A number means an arbitrary variable, let's call it x.
Squared means we raise x to the 2nd power: x^2
The sum means we add x^2 to 14 to get our algebraic expression below:
[B]x^2 + 14[/B]

The sum of d and v, all multiplied by 8

The sum of d and v, all multiplied by 8
This is an algebraic expression.
The sum of d and v:
d + v
Multiply this sum by 8:
[B]8(d + v)[/B]

the sum of doubling a number and 100 which totals to 160

the sum of doubling a number and 100 which totals to 160
Take this algebraic expression in pieces:
[LIST=1]
[*]Let the number be n.
[*]Double it, means we multiply n by 2: 2n
[*]The sum of this and 100 means we add 100 to 2n: 2n + 100
[*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160
[/LIST]
[B]2n + 100 = 160[/B] <-- This is our algebraic expression
If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]n = 30[/B]

The sum of five and twice a number is 17

The sum of five and twice a number is 17
[U]The phrase a number means an arbitrary variable, let's call it x[/U]
x
[U]Twice a number means we multiply x by 2:[/U]
2x
[U]The sum of five and twice a number means we add 5 to 2x:[/U]
2x + 5
[U]The phrase [I]is[/I] means an equation, so we set 2x + 5 equal to 17 to get our algebraic expression[/U]
[B]2x + 5 = 17[/B]
[B][/B]
As a bonus, if the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D17&pl=Solve']type in this algebraic expression into our math engine[/URL] and we get:
x = 6

The sum of m and 3 divided by the difference of m minus 3

The sum of m and 3 divided by the difference of m minus 3.
Sum of m and 3:
m + 3
Difference of m minus 3
m - 3
Take a quotient of these expressions:
[B]m + 3
-------
m - 3[/B]

the sum of n and twice n is 12

Twice n means we multiply n by 2
2n
The sum of n and twice n means we add
n + 2n
The word [I]is[/I] means equal to, so we set that expression above equal to 12
n + 2n = 12
Combine like terms:
3n = 12
Divide each side of the equation by 3 to isolate n
n = 4
Check our work
Twice n is 2*4 = 8
Add that to n = 4
8 + 4
12

the sum of the cube of a number and 12

the sum of the cube of a number and 12
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
Finally, we take the sum of x^3 and 12. Meaning, we add 12 to x^3. This is our final algebraic expression.
[B]x^3 + 12[/B]

the sum of the squares of a and b

the sum of the squares of a and b
Square of a means we raise a to the 2nd power:
a^2
Square of b means we raise b to the 2nd power:
b^2
The sum of squares means we add these terms together to get our algebraic expression:
[B]a^2 + b^2[/B]

The sum of the sum of x and z and the difference of y and z

The sum of the sum of x and z and the difference of y and z
Take this algebraic expression in 3 parts:
Step 1: The sum of x and z is written as:
x + z
Step 2: The difference of y and z is written as:
y - z
Step 3: the sum of the sum and difference is written as:
x + z + (y - z)
x + z + y - z
Cancelling the z terms, we get:
[B]x + y
[MEDIA=youtube]bmoZXImYCrg[/MEDIA][/B]

The sum of twice an integer and 3 times the next consecutive integer is 48

The sum of twice an integer and 3 times the next consecutive integer is 48
Let the first integer be n
This means the next consecutive integer is n + 1
Twice an integer means we multiply n by 2:
2n
3 times the next consecutive integer means we multiply (n + 1) by 3
3(n + 1)
The sum of these is:
2n + 3(n + 1)
The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48:
2n + 3(n + 1) = 48
Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48
We first need to simplify the expression removing parentheses
Simplify 3(n + 1): Distribute the 3 to each term in (n+1)
3 * n = (3 * 1)n = 3n
3 * 1 = (3 * 1) = 3
Our Total expanded term is 3n + 3
Our updated term to work with is 2n + 3n + 3 = 48
We first need to simplify the expression removing parentheses
Our updated term to work with is 2n + 3n + 3 = 48
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(2 + 3)n = 5n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
5n + 3 = + 48
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 48. To do that, we subtract 3 from both sides
5n + 3 - 3 = 48 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
5n = 45
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5n/5 = 45/5
Cancel the 5's on the left side and we get:
n = [B]9[/B]

The sum of two consecutive integers plus 18 is 123

The sum of two consecutive integers plus 18 is 123.
Let our first integer be n and our next integer be n + 1. We have:
n + (n + 1) + 18 = 123
Group like terms to get our algebraic expression:
2n + 19 = 123
If we want to solve the algebraic expression using our [URL='http://www.mathcelebrity.com/1unk.php?num=2n%2B19%3D123&pl=Solve']equation solver[/URL], we get n = 52. This means the next integer is 52 + 1 = 53

The sum of two y and the quantity of three plus y plus twice the quantity two y minus two equals fif

The sum of two y and the quantity of three plus y plus twice the quantity two y minus two equals fifteen
The sum of two y and the quantity of three plus y
2y + (3 + y)
twice the quantity two y minus two
2(2y - 2)
The sum of two y and the quantity of three plus y plus twice the quantity two y minus two
2y + (3 + y) + 2(2y - 2)
Equals 15 to get our algebraic expression
[B]2y + (3 + y) + 2(2y - 2) = 15[/B]
[B][/B]
If the problem asks you to solve for yL
2y + 3 + y + 4y - 4 = 15
Group like terms:
7y - 1 = 15
Add 1 each side:
7y = 16
Divide each side by 7:
y = [B]16/7[/B]

The sum of two y and three is the same as the difference of three y and one

The sum of two y and three
2y + 3
the difference of three y and one
3y - 1
is the same as means equal to. Set 2y + 3 equal to 3y - 1 for our final algebraic expression:
[B]2y + 3 = 3y - 1[/B]
[B][/B]
If the problem asks you to solve for y, subtract 2y from each side:
3 = y - 1
Add 1 to each side:
y = [B]4[/B]

the sum of x and 3 is divided by 2

the sum of x and 3 is divided by 2
The sum of x and 3
x + 3
Divide this expression by 2
(x + 3)/2

The sum of x and one half of x

The sum of x and one half of x
To write this algebraic expression correctly, we have (1 + 1/2)x
To get common denominators, we write 1 as 2/2. So we have:
(2/2 + 1/2)x
[B]3/2x[/B]

The sum of y and z decreased by the difference of m and n

The sum of y and z decreased by the difference of m and n.
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of y and z means we add z to y: y + z
[*]The difference of m and n means we subtract n from m: m - n
[*]The phrase [I]decreased by[/I] means we subtract the quantity (m - n) from the sum (y + z)
[/LIST]
[B](y + z) - (m - n)[/B]

the total of a and 352 equals a divided by 195

the total of a and 352 equals a divided by 195
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The total of a and 352 means we add 352 to a: a + 352
[*]a divided by 195: a/195
[*]The phrase [I]equals[/I] means we set (1) equal to (2) to get our final algebraic expression:
[/LIST]
[B]a + 352 = a/195[/B]

There are 12 eggs in a dozen. Write an algebraic expression for the number of eggs in d dozen.

There are 12 eggs in a dozen. Write an algebraic expression for the number of eggs in d dozen.
[B]12d[/B]

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping?
3/8 of the day means we take 3/8 of 24 also written as:
3/8 * 24
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F8&frac2=24&pl=Multiply']type this expression into our search engine [/URL]and get:
[B]9 hours[/B]

There are 76 milligrams of cholesterol in a 3.2 ounce serving of lobster. How much cholesterol is in

There are 76 milligrams of cholesterol in a 3.2 ounce serving of lobster. How much cholesterol is in a 6 ounce serving?
Let x equal the amount of cholesterol in milligrams for a 6 ounce service. Set up a proportion:
76/3.2 = x/6
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=76&num2=x&den1=3.2&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] by plugging that expression into the search engine, we get x = 142.5

There are thrice as many girls (g) as there are boys (b)

There are thrice as many girls (g) as there are boys (b)
Thrice means we multiply by 3, so we have the following algebraic expression:
[B]g = 3b[/B]

There was 35 balloons at the beginning of a party. By the end of the party, n of them had popped. Us

There was 35 balloons at the beginning of a party. By the end of the party, n of them had popped. Using n, write an expression for the number of balloons that were left.
We start with 35, we take away or subtract n that popped. We're left with:
[B]35 - n[/B]

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quo

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number
Let's call our number n.
Double the number means we multiply n by 2:
2n
Subtract 6 from the result means we subtract 6 from 2n:
2n - 6
Divide the answer by 2:
(2n - 6)/2
We can simplify this as n - 3
The quotient will be 20. This means the simplified term above is set equal to 20:
[B]n - 3 = 20 [/B] <-- This is our algebraic expression
If you want to take it a step further, and solve for n in the algebraic expression above, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-3%3D20&pl=Solve']type this expression into our calculator[/URL], and get:
n = 23

Thirty is half of the sum of 4 and a number

Thirty is half of the sum of 4 and a number.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of 4 and a number:
4 + x
Half of this sum means we divide by 2:
(4 + x)/2
Set this equal to 30:
[B](4 + x)/2 = 30[/B] <-- This is our algebraic expression

Three x is five less than twice x

Twice x means we multiply x by 2:
2x
five less than twice x
2x - 5
Three x
3x
The word [I]is[/I] means equal to. Set 2x - 5 equal to 3x for our algebraic expression:
[B]2x - 5 = 3x
[/B]
If the problem asks you to solve for x, subtract 2x from each side
[B]x = -5[/B]

Tickets to the amusement park cost $12 for adults and $8 for kids. Write on algebraic expression to

Tickets to the amusement park cost $12 for adults and $8 for kids. Write on algebraic expression to show the cost of a adult and k kids
Since cost = price * quantity, we have:
[B]12a + 8k[/B]

translate the product of -1 and a number in mathematics expression

translate the product of -1 and a number in mathematics expression
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The product of -1 and the number;
[B]-x[/B]

Translate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the varia

Translate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the variable m to represent Mais savings.
Twice means multiply by 2
2m
57 decreased by means subtract 2m from 57
[B]57 - 2m[/B]

Translate this phrase into an algebraic expression. 58 decreased by twice Gails age. Use the variabl

Translate this phrase into an algebraic expression. 58 decreased by twice Gails age. Use the variable g to represent Gails age.
Twice Gail's age:
2g
58 decreased by twice Gail's age
[B]58 - 2g[/B]

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to represent Gregs age.
The sum of 17 and Greg's age:
g + 17
The word [I]is[/I] means equal to, so we set g + 17 equal to 43
[B]g + 17 = 43[/B] <-- This is our algebraic expression
If you want to solve this equation for g, use our [URL='http://www.mathcelebrity.com/1unk.php?num=g%2B17%3D43&pl=Solve']equation calculator[/URL].
[B]g = 26[/B]

triple c divide the result by a

triple c divide the result by a
Take this algebraic expression in pieces.
Triple c means we multiply the variable c by 3
3c
Divide the result by a, means we take 3c, and divide by a
[B]3c/a[/B]

triple the sum of 36 and 6 then add 4

triple the sum of 36 and 6 then add 4
Take this algebraic expression in parts:
The sum of 36 and 6:
36 + 6
Triple the sum means we multiply the sum by 3:
3(36 + 6)
Then add 4:
[B]3(36 + 6) + 4[/B]
If the problem asks you to simplify the algebraic expression, we have:
3(42) + 4
126 + 4
[B]130[/B]

triple the value of c plus 3 is 84

Triple the value of c means we multiply c by 3
3c
Plus 3 means we add 3
3c + 3
Is, means equal to, so we set our expression equal to 84
[B]3c +3 = 84
[/B]
If you want to solve that equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3c%2B3%3D84&pl=Solve']equation solver[/URL]:
c = 27

tripled square of the difference of a and b

The difference of a and b is written as:
a - b
Square the difference means raise the difference to the power of 2
(a - b)^2
Triple this expression means multiply by 3:
[B]3(a - b)^2[/B]

Twenty-five is nine more than four times a number

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Four times a number:
4x
nine more than four times a numbrer
4x + 9
The phrase [I]is[/I] means equal to. We set 4x + 9 equal to 25 as our algebraic expression:
[B]4x + 9 = 25
[/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D25&pl=Solve']type it in our math solver[/URL] and get:
x = [B]4[/B]

Twenty-five is the same as ten added to twice a number

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
ten added to twice a number
2x + 10
The phrase [I]is the same as [/I]means equal to. Set 25 equal to 2x + 10 to get our algebraic expression
[B]25 = 2x + 10
[/B]
If the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=25%3D2x%2B10&pl=Solve']type it in our math solver [/URL]and get
x = [B]7.5[/B]

Twice a number decreased by eight is zero

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number:
2x
decreased by eight
2x - 8
[I]is [/I]means equal to. Set 2x - 8 equal to zero for our algebraic expression:
[B]2x - 8 = 0
[/B]
If the problem asks you to solve for x, add 8 to each side:
2x = 8
Divide each side by 2:
x= [B]4[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2.
We've got 2 algebraic expressions here. Let's take them in parts.
Left side algebraic expression: twice the difference of a number and 3
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]difference[/I] means we subtract 3 from the variable x
[*]x - 3
[*]Twice this difference means we multiply (x - 3) by 2
[*]2(x - 3)
[/LIST]
Right side algebraic expression: 3 times the sum of a number and 2
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]sum[/I] means we add 2 to the variable x
[*]x + 2
[*]3 times the sum means we multiply (x + 2) by 3
[*]3(x + 2)
[/LIST]
Now, we have both algebraic expressions, the problem says [I]is equal to[/I]
This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer
[B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8
Take this algebraic expression in pieces.
Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The difference of this number and 55 means we subtract 55 from x
x - 55
Twice the difference means we multiply x - 55 by 2
2(x - 55)
Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 8 means we add 8 to x
x + 8
3 times the sum means we multiply x + 8 by 3
3(x + 8)
Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side:
[B]2(x - 55) = 3(x + 8)[/B]

Twice the quantity of seven plus x is the same as the difference of x and seven

seven plus x
7 + x
Twice the quantity of seven plus x
2(7 + x)
Difference of x and seven
x - 7
The phrase [I]is the same as[/I] means equal to. This is our algebraic expression:
[B]2(7 + x) = x - 7
[/B]
If the problem asks you to solve for x, distribute 2 on the left side:
14 + 2x = x - 7
Subtract x from the right side
14 + x = -7
Subtract 14 from each side
[B]x = -21[/B]

twice the square of the product of x and y

twice the square of the product of x and y
Take this algebraic expression in pieces:
[LIST]
[*]The product of x and y means we multiply x and y: xy
[*]The square of the product means we raise xy to the power of 2: (xy)^2 = x^2y^2
[*]Twice the square means we multiply the square by 2: [B]2x^2y^2[/B]
[/LIST]

Twice x increased by the cube of y equals z

Twice x increased by the cube of y equals z
[LIST]
[*]Twice x means we multiply x by 2: 2x
[*]Increased this by the cube of y which is y^3. So we have 2x + y^3
[*]Now, we set this entire expression equal to z: 2x + y^3 = z
[/LIST]

u and 201 more equals q

201 more means we add:
u + 201
We set that expression equal to q
u + 201 = q

v equals 66 decreased by d

66 decreased by d means we subtract:
66 - d
v equals means we set our entire expression equal to v
[B]66 - d = v[/B]

v is equal to the product of 7 and the sum of u and 6

v is equal to the product of 7 and the sum of u and 6
[LIST]
[*]Sum of u and 6: u + 6
[*]the product of 7 and the sum of u and 6: 7(u + 6)
[*]We set this expression equal to v:
[/LIST]
[B]v = 7(u + 6)[/B]

Verbal Phrase

Free Verbal Phrase Calculator - Given an algebraic expression, this translates back to a verbal phrase

vw^2+y=x for w

vw^2+y=x for w
This is an algebraic expression.
Subtract y from each side:
vw^2 + y - y = x - y
The y's cancel on the left side, so we're left with:
vw^2 = x - y
Divide each side by v
w^2 = (x - y)/v
Take the square root of each side:
w = [B]Sqrt((x - y)/v)[/B]

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the oran

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the orange juice costs $1.50, write the expression for the total cost (in cents) for the food and drink
The cost C is:
C = 2x + 1.50(1)
Simplify:
[B]C = 2x + 1.50[/B]

What is the sum of a number x and y raised to the power of two in algebraic expression

What is the sum of a number x and y raised to the power of two in an algebraic expression?
The sum of a number x and y:
x + y
Raise this to the power of 2
(x + y)^2

what two values can d have if d squared is 9

what two values can d have if d squared is 9
d^2 = 9
Using [URL='https://www.mathcelebrity.com/radex.php?num=sqrt(9%2F1)&pl=Simplify+Radical+Expression']our calculator[/URL], we get:
d = [B](-3, 3}[/B]

When 20 is subtracted from 3 times a certain number, the result is 43

A certain number means an arbitrary variable, let's call it x
x
3 times x
3x
20 is subtracted from 3 time x
3x - 20
The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression
[B]3x - 20 = 43
[/B]
If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]:
[B]x = 21[/B]

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number
The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x".
4 times a number, increased by 40, means we multiply 4 times x, and then add 40
4x + 40
100 decreased by the number means we subtract x from 100
100 - x
The problem tells us both of these expressions are the same, so we set them equal to each other:
4x + 40 = 100 - x
Add x to each side:
4x + x + 40 = 100 - x + x
The x's cancel on the right side, so we have:
5x + 40 = 100
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 54 is subtracted from the square of a number, the result is 3 times the number.

When 54 is subtracted from the square of a number, the result is 3 times the number.
This is an algebraic expression. Let's take it in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
x
Square the number, means raise it to the 2nd power:
x^2
Subtract 54:
x^2 - 54
The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3
[B]x^2 - 54 = 3[/B]

When 9 is subtracted from 5 times a number ,the result is 31

When 9 is subtracted from 5 times a number ,the result is 31
A number means an arbitrary variable, let's call it x.
5 times this number is written as 5x.
9 subtracted from this is written as 5x - 9
[I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression.
Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

When a number is doubled, the result is 36

Excited to announce these types of algebraic expressions can be [URL='http://www.mathcelebrity.com/algexpress.php?num=whenanumberisdoubled,theresultis36&pl=Write+Expression']typed directly in our search engine[/URL].

When twice a number is reduced by 15 you get 95 what is the number

When twice a number is reduced by 15 you get 95 what is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
[I]Twice[/I] x means we multiply x by 2
2x
[I]Reduced by[/I] 15 means we subtract 15
2x - 15
[I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95
2x - 15 = 95 <-- This is our algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].

Which of the following is equivalent to the sum of the expression a^2 - 1 and a + 1?

Which of the following is equivalent to the sum of the expression a^2 - 1 and a + 1?
A) a^2 + a
B) a^3 - 1
C) 2a^2
D) a^3
a^2 - 1 + a + 1
The 1's cancel, so we're left with:
[B]a^2 + a - Answer A[/B]

Word Notation

Free Word Notation Calculator - Calculates the following:

* The word notation of a number of numeric expression

* The word notation of a number of numeric expression

write an algebraic expression for 197 times y

write an algebraic expression for 197 times y
[B]197y
[/B]
This can also be found by typing 197 times y into our search engine

Write an algebraic expression for 8 multiplied by the result of u reduced by 11.

Write an algebraic expression for 8 multiplied by the result of u reduced by 11.
u [I]reduced by[/I] 11
Reduced by means subtract 11 from u. So we have:
u - 11
We multiply this expression by 8 to get our algebraic expression of:
[B]8(u - 11)[/B]

Write an expression for the amount of money in p pennies plus 7 dollars.

Write an expression for the amount of money in p pennies plus 7 dollars.
Each penny is worth 0.01, so we have:
[B]0.01p + 7d[/B]

Write the verbal expression for: 9x

Write the verbal expression for: 9x
Using our [URL='http://www.mathcelebrity.com/verbalphrase.php?num=9x&pl=Verbal+Phrase']verbal expression calculator[/URL], we get either of the following:
[LIST]
[*][B]9 times x[/B]
[*][B]9 multiplied by x[/B]
[/LIST]

x add y, multiply by z then subtract d

x add y, multiply by z then subtract d
Take this algebraic expression in pieces:
[LIST]
[*]x add y: x + y
[*]multiply by z: z(x + y)
[*]Subtract d: [B]z(x + y) - d[/B]
[/LIST]

X is a natural number greater than 6

I saw this ticket come through today.
The answer is x > 6.
Natural numbers are positive numbers not 0. So 1, 2, 3, ...
Let me build this shortcut into the calculator.
Also, here is the[URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E6&pl=Show+Interval+Notation'] interval notation[/URL] for that expression.

X is at least as large as 4

X is at least as large as 4.
This is an algebraic expression, where the phrase [I]at least as large as[/I] means greater than or equal to:
[B]x >=4[/B]

y minus 10 is equal to the product of y and 8

y minus 10 is equal to the product of y and 8.
Take this algebraic expression in 3 parts:
Part 1: y minus 10
Subtract 10 from the variable y
y - 10
Part 2: The product of y and 8
We multiply 8 by the variable y
8y
Part 3: The phrase [I]is equal to[/I] means an equation, so we set y - 10 equal to 8y
[B]y - 10 = 8y[/B]

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the total number of baseball cards he has now.
144 and m more means we add
[B]144 + m[/B]

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the t

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the total number of baseball cards he has now.
9 more means we add 9 to n
[B]n + 9[/B]

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost fo

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost for n people to go to the park all day is given by the expression 7n. 8 friends go to the park on Saturday. What is the total cost of admission?
We want to evaluate f(n) = 7n for n = 8
f(8) = 7(8) = [B]56[/B]

You and some friends are going to the fair. Each ticket for a ride costs $0.75. If n is the number o

You and some friends are going to the fair. Each ticket for a ride costs $0.75. If n is the number of tickets purchased, write an expression that gives the total cost of buying n tickets.
We know cost = Price * Quantity, so we have:
Cost of buying n tickets = [B]0.75n[/B]

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $2 for a ticket. Write an expression for the total cost of going to Cedar Point where r is the number of rides.
Set up the cost equation C(r):
C(r) = Cost per ride * r rides + Park Fee
[B]C(r) = 2r + 50[/B]

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long will it be until you have $11,100 to buy a boat. Round to the next higher month.
[U]Set up our accumulation expression:[/U]
270(1.03)^n = 11100
1.03^n = 41.1111111
[U]Take the natural log of both sides[/U]
n * Ln(1.03) = 41.1111111
n = 3.71627843/0.0295588
n = 125.72 so round up to [B]126[/B]

You started this year with $491 saved and you continue to save an additional $11 per month. Write an

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Set up a savings function for m months
[B]S(m) = 491 + 11m[/B]

You work for a remote manufacturing plant and have been asked to provide some data about the cost of

You work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls?
We've got 2 questions here.
Question 1: We want the cost function C(r) where r is the number of remotes:
C(r) = Variable Cost per unit * r units + Fixed Cost (labor)
[B]C(r) = 3r + 2000
[/B]
Question 2: What is the cost of producing 2000 remote controls.
In this case, r = 2000, so we want C(2000)
C(2000) = 3(2000) + 2000
C(2000) = 6000 + 2000
C(2000) = [B]$8000[/B]

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours?

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours?
If your pay is rate times hours, we have:
[B]7h[/B]

z , subtract 5 then times by 3

z , subtract 5 then times by 3
Take this algebraic expression two parts:
[LIST]
[*]z subtract 5: z - 5
[*][I]Then times by 3[/I] means we multiply the expression z - 5 by 3
[/LIST]
[B]3(z - 5)[/B]

z fewer than the difference of 5 and y

z fewer than the difference of 5 and y
Take this algebraic expression in parts:
The difference of 5 and y means we subtract y from 5
5 - y
z fewer than this difference means we subtract z from 5 - y
[B]5 - y - z[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same a

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x):
[U]She subtracts 6 then multiplies the result by 5[/U]
[LIST]
[*]Subtract 6: x - 6
[*]Multiply the result by 5: 5(x - 6)
[/LIST]
[U]She subtracts 5 from the number then multiplying by 4[/U]
[LIST]
[*]Subtract 6: x - 5
[*]Multiply the result by 5: 4(x - 5)
[/LIST]
Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation:
5(x - 6) = 4(x - 5)
Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]10[/B]