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Inequalities worksheet

Grade 6 math, Common Core 6.EE.B.8. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Inequalities

Grade 6 math, Common Core 6.EE.B.8

Write or solve each inequality.

  1. 1.
    Is 2 a solution of 3x + 8 > 40?
  2. 2.
    Write an inequality: a number x is at least 49.
  3. 3.
    Is 9 a solution of 3x + 4 > 24?
  4. 4.
    Is 12 a solution of 3x + 6 > 16?
  5. 5.
    Solve: 9x < 63
  6. 6.
    Solve: 3x < 27
  7. 7.
    Is 11 a solution of 3x + 9 > 15?
  8. 8.
    Write an inequality: More than 6 people came to the game. Use p for people.
  9. 9.
    Write an inequality: a number x is at most 33.
  10. 10.
    Solve: x − 3 ≥ 14
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Inequalities

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. No

    3(2) + 8 = 1414 ≤ 40

  2. 2. x ≥ 49

  3. 3. Yes

    3(9) + 4 = 3131 > 24

  4. 4. Yes

    3(12) + 6 = 4242 > 16

  5. 5. x < 7

    Divide both sides by 9

  6. 6. x < 9

    Divide both sides by 3

  7. 7. Yes

    3(11) + 9 = 4242 > 15

  8. 8. p > 6

  9. 9. x ≤ 33

  10. 10. x ≥ 17

    Add 3 to both sides

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About inequalities

An inequality says one amount is greater than or less than another, using >, <, ≥ (greater than or equal to) or ≤ (less than or equal to). It usually has many solutions: x > 5 is true for 6, 7, 5.5 and every other number bigger than 5. Solve a one-step inequality the same way as an equation.

Worked example 1

Solve: 6x ≤ 48
  1. Step 1.Divide both sides by 6

Answer: x ≤ 8

Worked example 2

Is 7 a solution of 3x + 2 > 12?
  1. Step 1.3(7) + 2 = 23
  2. Step 2.23 > 12

Answer: Yes

Worked example 3

Solve: 3x ≤ 15
  1. Step 1.Divide both sides by 3

Answer: x ≤ 5

Watch out for

  • “At least” means ≥ and “at most” or “no more than” means ≤.
  • The small end of the symbol points to the smaller amount.
  • Test a number from your answer in the original inequality to check it.

Practice inequalities online

On StudyWiz, your kid can practice inequalities with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

More grade 6 math worksheets

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See all 6th grade math worksheets, or switch to grade 7 or grade 8.

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