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Grade 7 Math · Inequalities

Grade 7 Inequalities Practice Test

Build Grade 7 Math skills with five 10-question practice tests on solving inequalities, number-line graphs, compound inequalities, and real-world situations.

Inequalities Practice Tests

These Grade 7 Math practice tests help students solve and interpret inequalities. Students work with one-step and two-step inequalities, negative coefficients, number-line representations, compound inequalities, and practical constraints.

Skills covered

  • Solving one-step and two-step inequalities
  • Reversing the inequality sign when multiplying or dividing by a negative number
  • Reading open and closed circles on number lines
  • Writing compound inequalities and unions of intervals
  • Translating budget, temperature, distance, and quantity constraints
  • Checking whether a value belongs to a solution set

How to use these practice tests

Use inverse operations to isolate the variable. Remember that multiplying or dividing both sides by a negative number reverses the inequality sign. Use an open circle for a strict inequality and a closed circle when the endpoint is included.

For more Grade 7 Math practice, return to the Grade 7 Math category.

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5 Tests
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5. Test

Grade 7 Inequalities Practice Tests

A 10-question Grade 7 Math practice test on solving inequalities, reversing inequality signs, number-line graphs, compound inequalities, and real-world situations.

Use inverse operations to isolate the variable, reverse the inequality sign when multiplying or dividing by a negative number, and check a value from the solution set.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

You have xx dollars and spend $7. At least $10 remains. Which inequality describes the situation?

Please select an answer first.

Correct answer: A

The correct answer is x≥17x\ge17.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: The condition is x−7≥10x-7\ge10. Add 7 to get x≥17x\ge17.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

The condition is x−7≥10x-7\ge10. Add 7 to get x≥17x\ge17.

2. QuestionMultiple choice

A temperature tt drops by 8 degrees and becomes less than 0. Which inequality describes the original temperature?

Please select an answer first.

Correct answer: B

The correct answer is t<8t<8.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write t−8<0t-8<0. Add 8 to both sides: t<8t<8.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write t−8<0t-8<0. Add 8 to both sides: t<8t<8.

3. QuestionMultiple choice

A score plus 12 must be at least 75. What scores satisfy the inequality?

Please select an answer first.

Correct answer: C

The correct answer is s≥63s\ge63.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write s+12≥75s+12\ge75. Subtract 12: s≥63s\ge63.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write s+12≥75s+12\ge75. Subtract 12: s≥63s\ge63.

4. QuestionMultiple choice

Five times a number is no more than 40. What values can the number have?

Please select an answer first.

Correct answer: D

The correct answer is n≤8n\le8.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write 5n≤405n\le40. Divide by 5: n≤8n\le8.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write 5n≤405n\le40. Divide by 5: n≤8n\le8.

5. QuestionMultiple choice

A ride costs $3 plus $2 per mile. If the budget is at most $15, how many miles can you travel?

Please select an answer first.

Correct answer: A

The correct answer is m≤6m\le6.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write 3+2m≤153+2m\le15. Subtract 3 and divide by 2: m≤6m\le6.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write 3+2m≤153+2m\le15. Subtract 3 and divide by 2: m≤6m\le6.

6. QuestionMultiple choice

A student must read at least 30 pages at 5 pages per day. How many days are needed?

Please select an answer first.

Correct answer: B

The correct answer is d≥6d\ge6.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write 5d≥305d\ge30. Divide by 5: d≥6d\ge6.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write 5d≥305d\ge30. Divide by 5: d≥6d\ge6.

7. QuestionMultiple choice

A rectangle has width 4 and length xx. Its perimeter is greater than 24. Which inequality describes the length?

Please select an answer first.

Correct answer: C

The correct answer is x>8x>8.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write 2x+2(4)>242x+2(4)>24. Then 2x>162x>16 and x>8x>8.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write 2x+2(4)>242x+2(4)>24. Then 2x>162x>16 and x>8x>8.

8. QuestionMultiple choice

You have $14 and earn $6 per chore. You need at least $50. How many chores are needed?

Please select an answer first.

Correct answer: D

The correct answer is c≥6c\ge6.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write 14+6c≥5014+6c\ge50. Subtract 14 and divide by 6: c≥6c\ge6.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write 14+6c≥5014+6c\ge50. Subtract 14 and divide by 6: c≥6c\ge6.

9. QuestionMultiple choice

Three times a number minus 5 is less than 28. Which inequality describes the number?

Please select an answer first.

Correct answer: A

The correct answer is n<11n<11.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write 3n−5<283n-5<28. Add 5 and divide by 3: n<11n<11.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write 3n−5<283n-5<28. Add 5 and divide by 3: n<11n<11.

10. QuestionMultiple choice

A temperature starts at -4 degrees and rises 3 degrees per hour. After how many hours will it be at least 8 degrees?

Please select an answer first.

Correct answer: B

The correct answer is h≥4h\ge4.

  1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
  2. Apply the inequality rule: Write −4+3h≥8-4+3h\ge8. Add 4 and divide by 3: h≥4h\ge4.
  3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Write −4+3h≥8-4+3h\ge8. Add 4 and divide by 3: h≥4h\ge4.

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Frequently asked questions about Grade 7 Inequalities

When should the inequality sign be reversed?

Reverse the inequality sign when multiplying or dividing both sides by a negative number.

What is the difference between open and closed circles?

An open circle represents a strict inequality such as less than or greater than. A closed circle represents an inclusive inequality such as less than or equal to or greater than or equal to.

How many questions are on this page?

The page includes five mini tests with 10 questions each, for 50 Grade 7 Inequalities questions in total.