arbitrary - A number which could be any number it is defined to be but for which no specific value is chosen.

-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 a number decreased by twice a number

1/2 of a number decreased by twice a number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]1/2 of a number: x/2
[*]Twice a number means we multiply x by 2: 2x
[*]The phrase [I]decreased by[/I] means we subtract
[/LIST]
[B]x/2 - 2x[/B]

1/3 a number increased by 10 times by that same number

1/3 a number increased by 10 times by that same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
1/3 a number
1/3 * x = x/3
That same number means the same arbitrary variable as above:
x
10 times that same number:
10x
The phrase [I]increased by[/I] means we add:
[B]x/3 + 10x
[MEDIA=youtube]29TGt3i28jw[/MEDIA][/B]

1/3 of the sum of a number and 2 plus 5 is -20

1/3 of the sum of a number and 2 plus 5 is -20
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
the sum of a number and 2:
x + 2
1/3 of the sum of a number and 2
1/3(x + 2)
1/3 of the sum of a number and 2 plus 5
1/3(x + 2) + 5
The phrase [I]is[/I] means equal to, so we set 1/3(x + 2) + 5 equal to -20:
[B]1/3(x + 2) + 5 = -20[/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]

10 more than a number z, divided by k

10 more than a number z, divided by k
The phrase [I]a number[/I] means an arbitrary variable, lets call it x.
10 more than a number means we add 10 to x:
x + 10
We divide this quantity by k:
[B](x + 10)/k[/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

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
12 multiplied by this number:
12x
The product of 12x is reduced by 9
12x - 9
The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37:
[B]12x - 9 = 37[/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

15 added to a number is 16 times the number

15 added to a number is 16 times the number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]15 added to a number: 15 + x
[*]16 times the number: 16x
[*]The phrase [I]is[/I] means equal to. So we set 15 + x equal to 16x
[/LIST]
[B]15 + x = 16x[/B]

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]

15 less than a number squared

15 less than a number squared
A number is denoted by an arbitrary variable, let's call it x.
x
Squared means we raise that number to a power of 2
x^2
15 less means we subtract
[B]x^2 -15[/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]

2 less than half a number

A number means we pick an arbitrary variable, let's call it "x".
Half a number is 1/2x.
2 less than that is [B]1/2x - 2[/B]

2 minus 7 times a number

A number is represented by an arbitrary variable, let's call it x.
7 times x means we multiply 7 times x.
7x
2 minus 7x is written:
2 - 7x

2 more than twice the sum of 10 and a number

2 more than twice the sum of 10 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of 10 and a number means we add x to 10:
10 + x
Twice the sum means we multiply 10 + x by 2:
2(10 + x)
2 more than twice the sum means we add 2 to 2(10 + x):
[B]2(10 + x) + 2[/B]

2 numbers that are equal have a sum of 60

2 numbers that are equal have a sum of 60
Let's choose 2 arbitrary variables for the 2 numbers
x, y
Were given 2 equations:
[LIST=1]
[*]x = y <-- Because we have the phrase [I]that are equal[/I]
[*]x + y = 60
[/LIST]
Because x = y in equation (1), we can substitute equation (1) into equation (2) for x:
y + y = 60
Add like terms to get:
2y = 60
Divide each side by 2:
2y/2 = 60/2
Cancel the 2's and we get:
y = [B]30
[/B]
Since x = y, x = y = 30
x = [B]30[/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 a number subtracted by x

2 times a number subtracted by x
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
n
2 times a number means we multiply n by 2:
2n
The phrase [I]subtracted by[/I] means we subtract 2n from x:
[B]x - 2n[/B]

2 times half of a number

A number means an arbitrary variable, let's call it x.
Half of x means we divide x by 2, or multiply by 0.5
x/2
2 times half x is written:
[B]2(x/2)[/B]
If we simplify by cancelling the 2's, we just get x.

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]

2 times the sum of a number and 3 is equal to 3x plus 4

2 times the sum of a number and 3 is equal to 3x plus 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 3 means we add 3 to x:
x + 3
2 times this sum means we multiply the quantity x + 3 by 2
2(x + 3)
3x plus 4 means 3x + 4 since the word plus means we use a (+) sign
3x + 4
The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4
[B]2(x + 3) = 3x + 4[/B]

2/3 of a number 17 is at least 29

2/3 of a number 17 is at least 29
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
2/3 of a number means we multiply x by 2/3:
2x/3
The phrase [I]is at least[/I] also means greater than or equal to, so we set up the inequality:
[B]2x/3 >= 29[/B]

2/5 the cube of a number

2/5 the cube of a number
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
2/5 of the cube means we multiply x^3 by 2/5:
[B](2x^3)/5[/B]

26 increased by 12 times a number

26 increased by 12 times a number
A number is represented by an arbitrary variable, let's call it x
12 times a number is written as 12x
26 increased by 12 times a number means we add:
[B]26 + 12x[/B]

28 less than twice a number

[U]A number means an arbitrary variable, let's call it x.[/U]
[LIST]
[*]x
[/LIST]
[U]Twice a number means multiply by 2[/U]
[LIST]
[*]2x
[/LIST]
[U]28 less than twice a number means we subtract 28[/U]
[LIST]
[*][B]2x - 28[/B]
[/LIST]

3 decreased by 7 times a number

3 decreased by 7 times a number
A number signifies an arbitrary variable, let's call it x.
7 times a number:
7x
3 decreased by this means we subtract 7x
[B]3 - 7x[/B]

3 is subtracted from square of a number

3 is subtracted from square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Square of a number means we raise x to the 2nd power:
x^2
3 is subtracted from square of a number
[B]x^2 - 3[/B]

3 less than a number times itself

3 less than a number times itself
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Itself means the same variable as above. So we have:
x * x
x^2
3 less than this means we subtract 3 from x^2:
[B]x^2 - 3[/B]

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 a number is 3 more a number

3 times a number is 3 more a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times a number:
3x
3 more than a number means we add 3 to x:
x + 3
The word [I]is[/I] means and equation, so we set 3x equal to x + 3
[B]3x = x + 3[/B]

30 increased by 3 times the square of a number

Let "a number" equal the arbitrary variable x.
The square of that is x^2.
3 times the square of that is 3x^2.
Now, 30 increased by means we add 3x^2 to 30
30 + 3x^2

30 increased by 3 times the square of a number

30 increased by 3 times the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The square of a number means we raise x to the power of 2:
x^2
3 times the square:
3x^2
The phrase [I]increased by[/I] means we add 3x^2 to 30:
[B]30 + 3x^2[/B]

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 cubed decreased by 7

4 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7

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 a number plus 9

A number means an arbitrary variable, let's call it "x".
4 times a number is 4x.
Plus 9 means we add:
4x + 9

4 times the difference of 6 times a number and 7

4 times the difference of 6 times a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times a number
6x
The difference of 6x and 7 means we subtract 7 from 6x:
6x - 7
Now we multiply this difference by 4:
[B]4(6x - 7)[/B]

4 times the quantity of a number plus 6

4 times the quantity of a number plus 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The word [I]plus[/I] means we addd 6 to x
x + 6
The phrase [I]4 times the quantity [/I]means we multiply x + 6 by 4
[B]4(x + 6)[/B]

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 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 more than twice the cube of a number

5 more than twice the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The cube of a number means we raise x to the power of 3:
x^3
Twice the cube means we multiply x^3 by 2
2x^3
Finally, 5 more than twice the cube means we add 5 to 2x^3:
[B]2x^3 + 5[/B]

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 13

5 times a number increased by 13
A number is denoted as an arbitrary variable, let's call it x
x
5 times that number
5x
Increased by 13 means we add
5x + 13

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 a number is 4 more than twice a number

5 times a number is 4 more than twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
5 times a number:
5x
Twice a number means we multiply x by 2:
2x
4 more than twice a number
2x + 4
The word [I]is[/I] means equal to, so we set 5x equal to 2x + 4
[B]5x = 2x + 4[/B]

5 times a number is that number minus 3

5 times a number is that number minus 3
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[LIST]
[*]5 times a number: 5x
[*]That number means we use the same number from above which is x
[*]That number minus 3: x - 3
[*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3
[/LIST]
[B]5x = x - 3[/B]

5 times the sum of 3 times a number and -5

5 times the sum of 3 times a number and -5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
3 times a number means we multiply x by 3:
3x
the sum of 3 times a number and -5 means we add -5 to 3x:
3x - 5
5 times the sum means we multiply 3x - 5 by 5:
[B]5(3x - 5)[/B]

51 decreased by twice a number

A number is denoted as an arbitrary variable, let's call it x.
Twice a number means we multiply by 2, so 2x.
51 decreased by twice a number means we subtract 2x from 51
[B]51 - 2x[/B]

6 is divided by square of a number

6 is divided by square of a number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
the square of this means we raise x to the power of 2:
x^2
Next, we divide 6 by x^2:
[B]6/x^2[/B]

6 plus twice the sum of a number and 7.

6 plus twice the sum of a number and 7.
The phrase [I]a number[/I] mean an arbitrary variable, let's call it x.
The sum of a number and 7 means we add 7 to the variable x.
x + 7
Twice the sum means we multiply the sum by 2:
2(x + 7)
6 plus means we add 6 to 2(x + 7)
[B]6 + 2(x + 7)[/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 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[/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]

7 is 1/4 of some number

7 is 1/4 of some number
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
1/4 of this is written as:
x/4
The word [I]is[/I] means an equation, so we set x/4 equal to 7:
[B]x/4 = 7[/B]

7 minus a number all divided by 4

7 minus a number all divided by 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 minus a number
7 - x
All divided by 4:
[B](7 - x)/4[/B]

7 plus the quantity of 9 increased by a number

7 plus the quantity of 9 increased by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
9 increased by a number means we add 9 to x
9 + x
7 plus this quantity means we add (9 + x) to 7
[B]7 + (9 + x)[/B]

7 times a number and 2 is equal to 4 times a number decreased by 8

7 times a number and 2 is equal to 4 times a number decreased by 8
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 times a number:
7x
and 2 means we add 2:
7x + 2
4 times a number
4x
decreased by 8 means we subtract 8:
4x - 8
The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8:
[B]7x + 2 = 4x - 8[/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 the quantity of 3 times a number reduced by 10

7 times the quantity of 3 times a number reduced by 10
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
3 times a number:
3x
Reduced by 10 means we subtract 10:
3x - 10
7 times this quantity:
[B]7(3x - 10)[/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 thrice a number

Thrice a number means we multiply by 3. A number means an arbitrary variable, let's call it x
3x
8 is subtracted from 3x
[B]3x - 8[/B]

8 is subtracted from twice a number

Twice a number:
[LIST]
[*]Choose an arbitrary variable, let's call it x
[*]Twice x means multiply by 2
[*]2x
[/LIST]
8 subtracted from 2x:
[B]2x - 8[/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 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 is the sum of 7 and twice a number

9 is the sum of 7 and twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice a number means we multiply x by 2:
2x
The sum of 7 and twice a number
7 + 2x
The word [I]is[/I] mean equal to, so we set 7 + 2x equal to 9:
[B]7 + 2x = 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 10

9 times a number is that number minus 10
The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x:
x
9 times a number means we multiply x by 9:
9x
The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x:
x
That number minus 10 means we subtract 10 from x:
x - 10
The word [I]is[/I] means equal to, so we set 9x equal to x - 10
[B]9x = x - 10[/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 first number plus twice a second number is 10. Twice the first number plus the second totals 35. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers.
[U]The phrase [I]a number[/I] means an arbitrary variable[/U]
A first number is written as x
A second number is written as y
[U]Twice a second number means we multiply y by 2:[/U]
2y
[U]A first number plus twice a second number:[/U]
x + 2y
[U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U]
x + 2y = 10
[U]Twice the first number means we multiply x by 2:[/U]
2x
[U]Twice the first number plus the second:[/U]
2x + y
[U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U]
2x + y = 35
Therefore, we have a system of two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 35
[/LIST]
Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -20
[*]2x + y = 35
[/LIST]
Because the x variables are opposites, we can add both equations together:
(-2 + 2)x + (-4 + 1)y = -20 + 35
The x terms cancel, so we have:
-3y = 15
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-5
[/B]
Now we substitute this y = -5 into equation 2:
2x - 5 = 35
To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get:
x = [B]20[/B]

a number added to 5 minus p

a number added to 5 minus p
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We add 5 minus p to this number x:
[B]x + 5 - p[/B]

a number added to the product of y and x

a number added to the product of y and x
Since we're already using the variables x and y, we choose another arbitrary variable for the phrase [I]a number.[/I]
a
The product of y and x isL
xy
Then add a:
[B]a + xy[/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 is twice another number

a number is twice another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
The phrase [I]another number [/I]means another arbitrary variable, let's call it y
Twice means we multiply y by 2:
2y
The phrase [I]is [/I]means an equation, so we set x equal to 2y:
[B]x = 2y[/B]

A number multiplied by 6 and divided by 5 give four more than a number?

A number multiplied by 6 and divided by 5 give four more than a number?
A number is represented by an arbitrary variable, let's call it x.
Multiply by 6:
6x
Divide by 5
6x/5
The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4.
6x/5 = x + 4
Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side:
6x(5)/5 = 5(x + 4)
The 5's cancel on the left side, giving us:
6x = 5x + 20
Subtract 5x from each side
[B]x = 20[/B]
Check our work from our original equation:
6x/5 = x + 4
6(20)/5 ? 20 + 4
120/5 ?24
24 = 24 <-- Yes, we verified our answer

a number of pennies splits into 4 equal groups

a number of pennies splits into 4 equal groups
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take x and divide it by 4 to get 4 equal groups:
[B]x/4[/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 variable tripled less 40

a variable tripled less 40
[I]A variable[/I] means we pick an arbitrary variable, let's call it x
x
Tripled means we multiply by 3
3x
Less 40 means we subtract 40:
[B]3x - 40[/B]

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]

cube root of a number and 7

cube root of a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Cube root of a number means we raise x to the 1/3 power:
x^1/3
And 7 means we add 7:
[B]x^1/3 + 7[/B]

Decrease 12 by a number

Decrease 12 by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take 12 and decrease it by x, meaning we subtract x from 12:
[B]12 - x[/B]

decrease a number by 7 and multiply by 6.

decrease a number by 7 and multiply by 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Decrease a number by 7:
x - 7
Multiply by 6
[B]6(x - 7)[/B]

Determine the formula of the given statement by following the procedures. Choose any number then add

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2
For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x.
Add 2:
x + 2
Multiply your answer to 3:
3(x + 2)
And minus 2 which means we subtract:
[B]3(x + 2) - 2[/B]

Divide a number by 10. Then, add 10.

Divide a number by 10. Then, add 10.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Divide the number by 10 mean we have a quotient, of x over 10
x / 10
Then, add 10:
[B](x / 10) + 10[/B]

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain
No, they are different, here's how:
First, the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 less than a number means we subtract 7 from x:
x - 7
A number less than 7 means we subtract x from 7:
7 - x
As you can see:
x - 7 <> 7 - x so [B]they are different[/B]

Fifty-two less than 75% of a number

Fifty-two less than 75% of a number
A number means an arbitrary variable, let's call it x.
75% of this is 0.75x
Fifty-two less is:
[B]0.75x - 52[/B]

Five less than a number is at least -7 and at most 7.

Five less than a number is at least -7 and at most 7.
A number signifies an arbitrary variable, let's call it x.
Five less than a number: x - 5
Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality:
[B]-7 <= x - 5 <= 7[/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]

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

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 3 times a number added to 2 is divided by the number plus 4 the result is 4/3

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3
Take this in pieces, where "a number" means an arbitrary variable, let's call it "x".
[LIST=1]
[*]3 times a number --> 3x
[*]3 times a number added to 2 --> 3x + 2
[*]The number plus 4 --> x + 4
[*]is divided by --> (3x + 2)/(x + 4)
[*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3
[/LIST]

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 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 9 is added to 1/3 of a number, the result is 15. What is the number?

If 9 is added to 1/3 of a number, the result is 15. What is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
1/3 of a number means we multiply x by 1/3:
x/3
9 is added to 1/3 of a number:
x/3 + 9
The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15
x/3 + 9 = 15
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]18[/B]

if 9 times a number is decreased by 6, the result is 111

if 9 times a number is decreased by 6, the result is 111
A number means an arbitrary variable, let's call it x.
9 times a number:
9x
Decreased by 6
9x - 6
The result is 11, this means we set 9x - 6 equal to 11
[B]9x - 6 = 11
[/B]
To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]

if a number is added to its square, it equals 20

if a number is added to its square, it equals 20.
Let the number be an arbitrary variable, let's call it n.
The square of the number means we raise n to the power of 2:
n^2
We add n^2 to n:
n^2 + n
It equals 20 so we set n^2 + n equal to 20
n^2 + n = 20
This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions:
[B]n = (-5, 4)[/B]

if a number is decreased by 5, and then the result is multiplied by 2, the result is 26

If a number is decreased by 5, and then the result is multiplied by 2, the result is 26
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
[I]Decreased by[/I] means we subtract 5 from x:
x - 5
Multiply the result by 2:
2(x - 5)
The result is 26 means we set 2(x - 5) equal to 26:
[B]2(x - 5) = 26[/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 the difference of a number and 4 is multiplied by 3 the result is 19

If the difference of a number and 4 is multiplied by 3 the result is 19
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference of a number and 4:
x - 4
The phrase [I]is multiplied by[/I] means we multiply x - 4 by 3:
3(x - 4)
The phrase [I]the result is[/I] means equals, so we set 3(x - 4) equal to 19
[B]3(x - 4) = 19
[MEDIA=youtube]Q8bnVJuWeVk[/MEDIA][/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]

multiply a number by 4 and then subtract the answer from 30

multiply a number by 4 and then subtract the answer from 30
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Multiply this number by 4:
4x
Subtract the answer from 30:
[B]30 - 4x[/B]

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and su

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
multiply a number by 6 and subtract 6:
6x - 6
Multiply a number by 3 and subtract 4:
3x - 4
The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4
6x - 6 = 3x - 4
To solve this equation for x, we type it in our search engine and we get:
x = [B]2/3[/B]

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.

Nine less than a number is no more than 8 and no less than 3

Nine less than a number is no more than 8 and no less than 3
A number is denoted as an arbitrary variable, let's call it x.
We have a double inequality:
[LIST=1]
[*]No more than 8 means less than or equal to 8
[*]No less than 3 means greater than or equal to 3
[/LIST]
[B]3 <= x <= 8[/B]

Nine times the sum of a number and 6

Nine times the sum of a number and 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 6 means we add 6 to x:
x + 6
9 times the sum:
[B]9(x + 6)[/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]

product of a number and its reciprocal is increased by 7

product of a number and its reciprocal is increased by 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Its reciprocal means we take the reciprocal of x:
1/x
product of a number and its reciprocal:
x * 1/x
x/x
The x's cancel giving us:
1
is increased by 7 means we add 7:
1 + 7
[B]8[/B]

quotient of the sum of 2 numbers and 6

quotient of the sum of 2 numbers and 6
The phrase [I]two numbers[/I] means we choose 2 arbitrary variables, let's call them x and y
x, y
The sum of 2 numbers:
x + y
quotient of the sum of 2 numbers and 6
[B](x + y)/6[/B]

Seven less than 1/4 of a number is 9.

Seven less than 1/4 of a number is 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
1/4 of a number means we multiply x by 1/4:
x/4
Seven less than this means we subtract 7 from x/4:
x/4 - 7
The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9:
[B]x/4 - 7 = 9[/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]

Six less than twice a number is at least -1 and at most 1

First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x.
Twice a number means we multiply it by 2.
2x
Six less than that means we subtract 6
2x - 6
Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number.
-1 <= 2x - 6 <= 1

square root of the sum of 2 variables

square root of the sum of 2 variables
The phrase [I]2 variables[/I] means we choose 2 arbitrary variables, let's call them x and y:
x, y
The sum of 2 variables means we add:
x + y
Square root of the sum of 2 variables is written as:
[B]sqrt(x + y)[/B]

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]

subtract half of a number from 10

subtract half of a number from 10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
half of a number means we divide x by 2:
x/2
subtract half of a number from 10
[B]10 - x/2[/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]

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 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 number and 9 is 27. Find that number

The difference between a number and 9 is 27. Find that number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference between a number and 9
x - 9
The word [I]is[/I] means equal to, so we set x - 9 equal to 27:
x - 9 = 27
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]36[/B]

The difference between the opposite of a number and 6.

The difference between the opposite of a number and 6.
The phrase [I]a number means[/I] an arbitrary variable, let's call it x.
x
The opposite of a number means we multiply by x by -1
-x
The phrase [I]the difference between[/I] means we subtract 6 from -x:
[B]-x - 6[/B]

The difference between the product of 4 and a number and the square of a number

The difference between the product of 4 and a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The product of 4 and a number:
4x
The square of a number means we raise x to the power of 2:
x^2
The difference between the product of 4 and a number and the square of a number:
[B]4x - x^2[/B]

the difference between triple a number and double a number

the difference between triple a number and double a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Triple a number means we multiply x by 3:
3x
Double a number means we multiply x by 2:
2x
The difference means we subtract 2x from 3x:
3x - 2x
Simplifying like terms, we have:
(3 - 2)x = [B]x[/B]

The difference of 25 and a number added to triple another number

The difference of 25 and a number added to triple another number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x:
x
The difference of 25 and a number means we subtract x from 25:
25 - x
The phrase [I]another number[/I] means a different arbitrary variable, let's call it y:
y
Triple another number means we multiply y by 3:
3y
The phrase [I]added to[/I] means we add 25 - x to 3y
[B]25 - x + 3y[/B]

the difference of 4 and the quotient of 18 and a number

the difference of 4 and the quotient of 18 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The quotient of 18 and a number means we divide 18 by the variable x.
18/x
The difference of 4 and the quotient above means we subtract 18/x from 4:
[B]4 - 18/x[/B]

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 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 twice a number and 9 is less than 22

The difference of twice a number and 9 is less than 22
The phrase a number, means an arbitrary variable, let's call it x.
x
Twice a number
2x
The difference of twice a number and 9
2x - 9
Is less than 22
[B]2x - 9 < 22[/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 quotient of 2 and the sum of a number and 1

The quotient of 2 and the sum of a number and 1.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of a number and 1 is written as:
x + 1
The word [I]quotient[/I] means a fraction. So we divide 2 by x + 1
2
--------
( x + 1)

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
[B](x + 4)/7 = 10[/B]

the quotient of a number and twice another number

the quotient of a number and twice another number
The phrase[I] a number [/I]means an arbitrary variable, let's call it x.
The phrase[I] another number [/I]means another arbitrary variable, let's call it y.
Twice means we multiply y by 2:2y
The quotient means we divide x by 2y:
[B]x/2y[/B]

the quotient of a variable and 7

the quotient of a variable and 7.
A variable means an arbitrary number, let's call it x.
A quotient means a fraction, where x is the numerator and 7 is the denominator:
[B] x
---
7[/B]

the quotient of the cube of a number x and 5

the quotient of the cube of a number x and 5
[LIST]
[*]A number means an arbitrary variable, let's call it x
[*]The cube of a number means raise it to the 3rd power, so we have x^3
[*]Quotient means we have a fraction, so our numerator is x^3, and our denominator is 5
[/LIST]
[B]x^3
----
5[/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 ten to a number

the ratio of ten to a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The ratio of 10 and this number x is written as:
[B]10/x[/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[/B]

The square of a number increased by 7 is 23

The square of a number increased by 7 is 23
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
The square of a number means we raise x to the power of 2:
x^2
[I]Increased by[/I] means we add 7 to x^2
x^2 + 7
The word [I]is[/I] means an equation. So we set x^2 + 7 equal to 23:
[B]x^2 + 7 = 23[/B]

The square of the difference of a number and 4

The square of the difference of a number and 4
A number means an arbitrary variable, let's call it x
The difference of a number and 4:
x - 4
The square of this difference:
[B](x - 4)^2[/B]

the sum of 2 times a number and -2, added to 4 times a number

the sum of 2 times a number and -2, added to 4 times a number.
The phrase, [I]a number[/I], means an arbitrary variable, let's call it x.
2 times a number
2x
The sum of means add, so we add -2, which is the same as subtracting 2
2x - 2
Now, we add 4 times x
2x - 2 + 4x
Combining like terms, we have:
(2 + 4)x - 2
[B]6x - 2[/B]

the sum of 3 numbers

Since no variable name is defined, we pick 3 arbitrary variables. Let's pick x, y, and z.
The sum of 3 numbers means we add them together:
x + y + z

the sum of 3 numbers

Let's choose 3 arbitrary variables, w, x, and y. We add them up:
[B]w + x + y[/B]

the sum of 3 numbers divided by its product

the sum of 3 numbers divided by its product
The phrase [I]3 numbers[/I] means we choose [I]3[/I] arbitrary variables. Let's call them x, y, z.
The sum of of these 3 numbers is:
x + y + z
The phrase [I]its product[/I] means we multiply all 3 arbitrary variables together:
xyz
Now, the phrase [I]divided by[/I] means we divide x + y + z by xyz:
[B](x + y + z)/xyz[/B]

The sum of 3 times the square of a number and negative 7

The sum of 3 times the square of a number and negative 7
[U]The phrase [I]a number[/I] means an arbitrary variable, let's call it x:[/U]
x
[U]The square of a number means we raise x to the power of 2:[/U]
x^2
[U]3 times the square of a number:[/U]
3x^2
[U]The sum of 3 times the square of a number and negative 7[/U]
[B]3x^2 - 7[/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 6 times a number and -8, added to 3 times a number

The sum of 6 times a number and -8, added to 3 times a number
The phrase "a number", means an arbitrary variable, let's call it x.
6 times a number:
6x
And means we add, so we have
6x - 8
Added to 3 times a number
6x - 8 + 3x
Combine like terms:
[B]9x - 8[/B]

the sum of a number and 16 is e

A number means an arbitrary variable, let's call it x.
The sum of x and 16 means we add:
x + 16
Is, means equal to, so we set x + 16 = e
x + 16 = e

The sum of a number and 34 times the number

The sum of a number and 34 times the number
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
34 times the number:
34x
The sum of a number and 34 times the number means we add both terms together:
x + 34x

The sum of a number and 5 all divided by 2 is 17

The sum of a number and 5 all divided by 2 is 17
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The sum of a number and 5:
x + 5
All divided by 2:
(x + 5)/2
The word [I]is[/I] means equal to, so we set (x + 5)/2 equal to 17:
[B](x + 5)/2 = 17[/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 its reciprocal is 5/2

the sum of a number and its reciprocal is 5/2
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal of the number means 1/x.
The sum means we add them:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 52
[B]x + 1/x = 52[/B]

The sum of a number and its reciprocal is 72

The sum of a number and its reciprocal is 72
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The reciprocal of the number is written as:
1/x
The sum of a number and its reciprocal means we add:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 72
[B]x + 1/x = 72[/B]

The sum of a number and its reciprocal is five.

The sum of a number and its reciprocal is five.
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The reciprocal of the number is 1/x.
The sum means we add them together:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 5
[B]x + 1/x = 5[/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 and twice its reciprocal is 3

The sum of a number and twice its reciprocal is 3
the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number means we take 1 over that number:
1/x
Twice the reciprocal means we multiply 1/x by 2:
2/x
The sum of a number and twice its reciprocal
x + 2/x
The word [I]is[/I] means equal to, so we set x + 2/x equal to 3
[B]x + 2/x = 3[/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 a number times 3 and 30 is less than 17

the sum of a number times 3 and 30 is less than 17
A number is denoted as an arbitrary variable, let's call it x.
x
Times 3 means we multiply x by 3:
3x
The sum of a number times 3 and 30 means we add 30 to 3x above
3x + 30
Is less than 17 means we have an inequality, so we set 3x + 30 less than 17
3x + 30 < 17
To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:

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 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 square of a number and 7 times a number

The sum of the square of a number and 7 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Square the number:
x^2
7 times the number means we multiply x by 7:
7x
The sum means we add x^2 and 7x
[B]x^2 + 7x[/B]

The Sum of three times a number and 18 is -39. Find the number

The Sum of three times a number and 18 is -39. Find the number.
A number means an arbitrary variable, let us call it x.
Three times x:
3x
The sum of this and 18:
3x + 18
Is means equal to, so we set 3x + 18 = -39
3x + 18 = -39
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]

The sum of two numbers multiplied by 9

Choose two variables as arbitrary numbers, let's say x and y
[U]The sum of x and y is:[/U]
x + y
[U]Multiply that by 9[/U]
[B]9(x + y)[/B]

thesumof9andanumber

We denoted a number using the arbitrary variable "x".
The sum of 9 and x is written:
x + 9 or 9 + x

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 subtracted from triple a number

Three subtracted from triple a number
A number means an arbitrary variable, let's call it x
x
Triple it
3x
Three subtracted from this
[B]3x - 3[/B]

total of a number and the square of a number

total of a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The square of a number means we raise x to the power of 2. x^2
The total means we add x squared to x:
[B]x + x^2[/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]

triple a number and another number

triple a number and another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Triple a number means we multiply x by 3:
3x
The phrase [I]another number[/I] means another arbitrary variable, let's call it y:
y
The word [I]and[/I] means we add y to 3x:
[B]3x + y[/B]

twice a number subtracted from the square root of the same number

twice a number subtracted from the square root of the same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Twice a number means we multiply x by 2:
2x
Square root of the same number:
sqrt(x)
twice a number subtracted from the square root of the same number
[B]sqrt(x) - 2x[/B]

twice the difference between x and 28 is 3 times a number

twice the difference between x and 28 is 3 times a number
The difference between x and 28:
x - 28
Twice the difference means we multiply x - 28 by 2:
2(x - 28)
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
3 times a number:
3x
The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x:
[B]2(x - 28) = 3x[/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 square root of a number increased by 5 is 23

twice the square root of a number increased by 5 is 23
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The square root of a number means we raise x to the 1/2 power:
sqrt(x)
the square root of a number increased by 5 means we add 5 to sqrt(x):
sqrt(x) + 5
twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2:
2(sqrt(x) + 5)
The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23:
[B]2(sqrt(x) + 5) = 23[/B]

two thirds of a number is no more than -10

two thirds of a number is no more than -10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Two thirds of a number mean we multiply x by 2/3:
2x/3
The phrase [I]no more than[/I] -10 means less than or equal to -10, so we have an inequality:
[B]2x/3 <= -10[/B]

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512
We set up an arbitrary number x.
Subtracted from is written as
-9876 - x
The phrase [I]to obtain[/I] means an equation, so we set -9876 - x equal to -9512
-9876 - x = -9512
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-9876-x%3D-9512&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]364[/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 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
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 times a number means we multiply x by 4:
4x
Increased by 40 means we add 40 to 4x:
4x + 40
100 decreased by the number means we subtract x from 100:
100 - x
The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x
4x + 40 = 100 - x
Solve for [I]x[/I] in the equation 4x + 40 = 100 - x
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4x and -x. To do that, we add x to both sides
4x + 40 + x = -x + 100 + x
[SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE]
5x + 40 = 100
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 40 and 100. To do that, we subtract 40 from both sides
5x + 40 - 40 = 100 - 40
[SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE]
5x = 60
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5x/5 = 60/5
x = [B]12[/B]
Check our work for x = 12:
4(12) + 40 ? 100 - 12
48 + 40 ? 100 - 12
88 = 88

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 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].

y is the sum of twice a number and 3

y is the sum of twice a number and 3
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
twice a number means we multiply x by 2:
2x
the sum of twice a number and 3:
2x + 3
The word [I]is[/I] means equal to, so we set 2x + 3 equal to y
[B]y = 2x + 3[/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]