inequality | MathCelebrity Forum

# inequality

1. ### 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...
2. ### 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 a number 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 not less than means greater than or equal to. We set 15x greater than prequel to 15 15x >= 15 <-- This...
3. ### Translate and solve: 30 times m is greater than −330. (Write your solution in interval notation.)

Translate and solve: 30 times m is greater than −330. (Write your solution in interval notation.) 30 times m: 30m is greater than -330 30m > -330 Using our equation and interval solver, we get: m > -11
4. ### Teresa buys candy that costs \$4per pound. She will spend less than\$36on candy.

Teresa buys candy that costs \$4per pound. She will spend less than\$36on candy. \$36/\$4 per pound = 9 pounds. Spending less than that is denoted as s for spend: s < 9
5. ### kelko buys candy that costs \$7 per pound. She will spend less than \$84 on candy. What are the possib

kelko buys candy that costs \$7 per pound. She will spend less than \$84 on candy. What are the possible numbers of pounds she will buy. Let p be the number of pounds Kelko buys. p < 84/7 p < 12
6. ### The temperature inside the lab refrigerator is no more than 35 . Use t to represent the temperature

The temperature inside the lab refrigerator is no more than 35 . Use t to represent the temperature (in ) of the refrigerator. The phrase no more than means less than or equal to. We have this inequality: t <= 35
7. ### Maria runs each lap in 5 minutes. She will run less than 7 laps today. What are the possible numbers

Maria runs each lap in 5 minutes. She will run less than 7 laps today. What are the possible numbers of minutes she will run today? Total Time < Laps * minutes per laps Total Time < 7 * 5 Total Time < 35
8. ### The distance to the nearest exit door is less than 100 feet. Use d to represent the distance (in fee

The distance to the nearest exit door is less than 100 feet. Use d to represent the distance (in feet) to the nearest exit door. Less than means we use the < sign: d < 100
9. ### Debra buys candy that costs 4 per pound. She will spend less than 20 on candy. What are the possible

Debra buys candy that costs 4 per pound. She will spend less than 20 on candy. What are the possible numbers of pounds she will buy? Set up an inequality using less than < and p for pounds: 4p < 20 Divide each side by 4: 4p/4 < 20/4 p < 5
10. ### Lucy is thinking of a number. The number is greater than two hundred twenty-five. Her number is less

Lucy is thinking of a number. The number is greater than two hundred twenty-five. Her number is less than 2 hundreds, 2 tens, and 7 ones. What is Lucy's number? Let the number be n. n > 225 Also: n < 2(100) + 2(10) + 7(1) n < 200 + 20 + 7 n < 227 Combine these, we get: 225 < n < 227 Only one...
11. ### Write a fraction with a denominator of 9. The fraction should be less than 1/2

Write a fraction with a denominator of 9. The fraction should be less than 1/2 Let n be the numerator. We have: n/9 < 1/2 multiply each side by 9: 9n/9 < 9/2 n < 9/2 Examples are 8/2, 7/2, 6/2, 5/2, 4/2, 3/2,
12. ### Rachel runs each lap in 6 minutes. She will run less than 8 laps today. What are the possible number

Rachel runs each lap in 6 minutes. She will run less than 8 laps today. What are the possible numbers of minutes she will run today Less than means an inequality. 6 minutes per lap * 8 laps = 48 minutes. If m is the number of minutes Rachel runs, then we have: m < 48
13. ### The construction crew has less than 7 days to complete the road repairs. Let d represent the number

The construction crew has less than 7 days to complete the road repairs. Let d represent the number of days left to complete the road repairs. Less than means we don't include 7: d < 7
14. ### You can spend at most \$35. If you buy 5 tickets, how much can you spend on each ticket

You can spend at most \$35. If you buy 5 tickets, how much can you spend on each ticket We're given the number of tickets as 5. We know cost = price * quantity Let p = price The phrase at most means less than or equal to, so we have: 5p <= 35 Plugging this inequality into our search engine...
15. ### Carmen has \$30 in store bucks and a 25% discount coupon for a local department store. What maximum d

Carmen has \$30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than \$60 before sales tax Let the original price be p. p Apply 25% discount first...
16. ### Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How man

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How many hours does Margaret work each week? Let h be the hours worked We know that hourly rate * h equals total earnings. The phrases at least and no more than signify inequalities, so we have: 450 <=...
17. ### The sum of 2x and y is at least 20

The sum of 2x and y is at least 20 The sum of 2x and y: 2x + y The phrase is at least means an inequality. We write this as >= or greater than or equal to: 2x + y >= 20
18. ### a more than b is greater than 6

a more than b is greater than 6 a more than b: b + a Is greater than 6 means an inequality using the > sign: b + a > 6
19. ### Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,

Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,but together they scored less than 9 goals. What are the possible number of goal Romnick scored? Let j be Joey's goals Let r by Romnick's goals We're given 1 equation and 1 inequality: r = j +...
20. ### The sum of 3 consecutive integers is greater than 30.

The sum of 3 consecutive integers is greater than 30. Let the first consecutive integer be n The second consecutive integer is n + 1 The third consecutive integer is n + 2 The sum is written as: n + n + 1 + n + 2 Combine like terms: (n + n + n) + (1 + 2) 3n + 3 The phrase greater than means...