Inequality Word Problems Homework: Solving Algebraic Inequalities, Slides of Elementary Mathematics

A set of algebraic inequality problems to be solved. Students are required to read the problem carefully, write a let statement, determine the appropriate symbol (<, >, =, or none), and solve the inequality. various examples and prompts for finding possible values, graph representations, and translating verbal expressions into algebraic inequalities.

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2021/2022

Uploaded on 09/07/2022

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Name_____________________________________________________ Period: __________
Represent each of the following as an algebraic inequality.
1) x is at most 30 ___________________
2) the sum of 5x and 2x is at least 14 ___________________
3) the product of x and y is less than or equal to 4 ___________________
4) 5 less than a number y is under 20 ___________________
1st: Read carefully and underline key words
2nd: Write a let statement
3rd: Determine whether to use , , , or
4th: Write and solve the inequality
5) If 5 times a number is increased by 4, the result is at least 19. Find the least possible
number that satisfies these conditions.
6) The sum of twice a number and 5 is at most 15. What are the possible values for the
number?
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Name_____________________________________________________ Period: __________

Represent each of the following as an algebraic inequality.

  1. x is at most 30 ___________________

  2. the sum of 5x and 2x is at least 14 ___________________

  3. the product of x and y is less than or equal to 4 ___________________

  4. 5 less than a number y is under 20 ___________________

1 st: Read carefully and underline key words

2 nd: Write a let statement

3 rd: Determine whether to use , , , or

4 th: Write and solve the inequality

  1. If 5 times a number is increased by 4, the result is at least 19. Find the least possible number that satisfies these conditions.

  2. The sum of twice a number and 5 is at most 15. What are the possible values for the number?

  1. The cost of a gallon of orange juice is $3.50. What is the maximum number of containers you can buy for $15?

  2. Three times a number increased by 8 is no more than the number decreased by 4. Find the number.

  3. Two-thirds of a number plus 5 is greater than 12. Find the number.

(4) Kathy swam 3 laps in the pool this week. She must swim more than 12 laps.

  1. The sum of a number and 81 is greater than the product of 3 and that number. What are the possible values for the number?

  2. Four times a number is greater than 48. What are the possible values for the number?

1. Read carefully and underline key words

2. Write a Let statement [e.g. let x = …]

3. Determined whether to use the =, >, <, sign

4. Write and solve the inequality

Recall four steps to help solve these types of problems:

1. The quotient of a number and 15 is no greater than 450. What are the

possible values for the number?

2. Keith and Michelle went out to dinner. The total cost of the meal, including

the tip, came to $53.70. If the combined tip came out to $9.60, and each

friend spent an equal amount, how much did each friend pay not including

the tip?

3. Jason is saving up to buy a digital camera that costs $490. So far, he saved

$175. He would like to buy the camera 3 weeks from now. What is the

equation used to represent how much he must save every week to have

enough money to purchase the camera?