Grade 6 Math · Inequalities: Introduction

Grade 6 Inequalities Introduction Practice Test

Build Grade 6 Math skills with five 10-question practice tests on inequality symbols, number lines, solution sets, inverse operations, negative factors, and real-world constraints.

Inequalities Introduction Practice Tests

These Grade 6 Math practice tests introduce inequalities as comparisons and ranges of possible values. Students practice less than, greater than, less than or equal to, greater than or equal to, number-line graphs, one-step inequality solving, negative factors, and real-world limits.

Skills covered

  • Reading and writing inequality symbols
  • Interpreting at least, at most, no more than, under, and greater than
  • Representing solution sets on number lines
  • Solving one-step addition and subtraction inequalities
  • Solving multiplication and division inequalities
  • Reversing the inequality symbol when multiplying or dividing by a negative
  • Applying inequalities to age, cost, capacity, temperature, time, and score constraints

How to use these practice tests

Read the comparison words and decide whether the endpoint is included. Use an open circle for a strict inequality and a closed circle for an inclusive inequality. Apply inverse operations to both sides, reverse the inequality when multiplying or dividing by a negative, and test a sample value from the solution set.

For more Grade 6 Math practice, return to the Grade 6 Math category.

3. Test

Grade 6 Inequalities Introduction Practice Tests

A 10-question Grade 6 Math practice test on inequality symbols, number lines, solution sets, inverse operations, negative factors, and real-world constraints.

Interpret the comparison symbol, solve using inverse operations, reverse the sign when multiplying or dividing by a negative, and check a sample value.

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

Solve 2x>102x > 10.

Please select an answer first.

Correct answer: A

The correct answer is x>5x > 5.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Divide by positive 2, so the inequality direction stays the same: x>5x > 5.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Divide by positive 2, so the inequality direction stays the same: x>5x > 5.

2. QuestionMultiple choice

Solve 3y≤123y \le 12.

Please select an answer first.

Correct answer: B

The correct answer is y≤4y \le 4.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Divide by positive 3: y≤12÷3=4y \le 12 \div 3 = 4.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Divide by positive 3: y≤12÷3=4y \le 12 \div 3 = 4.

3. QuestionMultiple choice

Solve −4a>12-4a > 12.

Please select an answer first.

Correct answer: C

The correct answer is a<−3a < -3.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Divide by negative 4 and reverse the inequality: a<12÷(−4)=−3a < 12 \div (-4) = -3.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Divide by negative 4 and reverse the inequality: a<12÷(−4)=−3a < 12 \div (-4) = -3.

4. QuestionMultiple choice

Solve −2b≤8-2b \le 8.

Please select an answer first.

Correct answer: D

The correct answer is bge−4b ge -4.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Divide by negative 2 and reverse the direction: bge8÷(−2)=−4b ge 8 \div (-2) = -4.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Divide by negative 2 and reverse the direction: bge8÷(−2)=−4b ge 8 \div (-2) = -4.

5. QuestionMultiple choice

Solve x÷5ge3x \div 5 ge 3.

Please select an answer first.

Correct answer: A

The correct answer is xge15x ge 15.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Multiply by positive 5: xge3×5=15x ge 3 \times 5 = 15.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Multiply by positive 5: xge3×5=15x ge 3 \times 5 = 15.

6. QuestionMultiple choice

Solve y÷(−3)<4y \div (-3) < 4.

Please select an answer first.

Correct answer: B

The correct answer is y>−12y > -12.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Multiply by negative 3 and reverse the inequality: y>4×(−3)=−12y > 4 \times (-3) = -12.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Multiply by negative 3 and reverse the inequality: y>4×(−3)=−12y > 4 \times (-3) = -12.

7. QuestionMultiple choice

Solve 0.5xle20.5x le 2.

Please select an answer first.

Correct answer: C

The correct answer is xle4x le 4.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Divide by positive 0.5: xle2÷0.5=4x le 2 \div 0.5 = 4.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Divide by positive 0.5: xle2÷0.5=4x le 2 \div 0.5 = 4.

8. QuestionMultiple choice

Solve a÷(−2)>5a \div (-2) > 5.

Please select an answer first.

Correct answer: D

The correct answer is a<−10a < -10.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Multiply by negative 2 and reverse the inequality: a<5×(−2)=−10a < 5 \times (-2) = -10.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Multiply by negative 2 and reverse the inequality: a<5×(−2)=−10a < 5 \times (-2) = -10.

9. QuestionMultiple choice

Solve −6mge18-6m ge 18.

Please select an answer first.

Correct answer: A

The correct answer is mle−3m le -3.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Divide by negative 6 and reverse the direction: mle18÷(−6)=−3m le 18 \div (-6) = -3.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Divide by negative 6 and reverse the direction: mle18÷(−6)=−3m le 18 \div (-6) = -3.

10. QuestionMultiple choice

Solve n÷4<−2n \div 4 < -2.

Please select an answer first.

Correct answer: B

The correct answer is n<−8n < -8.

  1. Read the inequality: Identify the comparison symbol and whether the endpoint is included.
  2. Solve or represent the condition: Multiply by positive 4: n<−2×4=−8n < -2 \times 4 = -8.
  3. Check a value: Test a boundary or sample value to confirm that it belongs or does not belong to the solution set.

Multiply by positive 4: n<−2×4=−8n < -2 \times 4 = -8.

Frequently asked questions about Grade 6 Inequalities: Introduction

What topics are covered?

The page covers comparison symbols, endpoint meaning, number-line graphs, one-step inequalities, negative factors, solution sets, and real-world constraints.

When does the inequality symbol reverse?

The inequality symbol reverses when both sides are multiplied or divided by a negative number.

How many questions are on this page?

The page includes five mini tests with 10 questions each, for 50 Grade 6 Inequalities Introduction questions in total.