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Worksheets›Grade 6›Expressions & equations›Solutions to inequalities

Solutions to Inequalities Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Grade 6CCSS 6.EE.B.5Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: x compared with a number

  1. 1.Which of these values of x are solutions of xxx >>> 9?9?9? 3,3,3, 5,5,5, 7,7,7, 9,9,9, 111111
  2. 2.Which of these values of x are solutions of xxx ≥\ge ≥ 11?11?11? 5,5,5, 7,7,7, 9,9,9, 11,11,11, 131313
  3. 3.Which of these values of x are solutions of xxx >>> 9?9?9? 8,8,8, 9,9,9, 10,10,10, 11,11,11, 121212
  4. 4.Which of these values of x are solutions of xxx <<< 9?9?9? 7,7,7, 8,8,8, 9,9,9, 10,10,10, 111111
  5. 5.You must be at least 454545 inches tall to ride a roller coaster: hhh ≥\ge ≥ 45.45.45. Which of these heights can ride? 43,43,43, 45,45,45, 47,47,47, 49,49,49, 515151
  6. 6.You must be at least 494949 inches tall to ride a roller coaster: hhh ≥\ge ≥ 49.49.49. Which of these heights can ride? 46,46,46, 49,49,49, 52,52,52, 55,55,55, 585858
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

An inequality usually has many solutions. Substitute each value, or first get x by itself, then keep the values that make the inequality true. Watch whether the boundary itself is included: ≤ and ≥ include it, < and > don't.

EasyYou must be at least 404040 inches tall to ride a roller coaster: hhh ≥\ge ≥ 40.40.40. Which of these heights can ride? 37,37,37, 40,40,40, 43,43,43, 46,46,46, 494949x compared with a numberMediumYou must be at least 505050 inches tall to ride a roller coaster: hhh ≥\ge ≥ 50.50.50. Which of these heights can ride? 41,41,41, 44,44,44, 47,47,47, 50,50,50, 535353x plus or minus a numberHardWhich of these values of x are solutions of 4x4x4x ≤\le ≤ 40?40?40? 7,7,7, 8,8,8, 9,9,9, 10,10,10, 111111A number times x

How to solve it: a worked example

List every value that is a solution.

  1. StartWhich of these values of x are solutions of xxx <<< 8?8?8? 2,2,2, 4,4,4, 6,6,6, 8,8,8, 101010
  2. Keep the values that make it true2,2,2, 4,4,4, 666
  3. Answer2,2,2, 4,4,4, 666

Common mistakes to watch for

  • Including the boundary value for < or >.
  • Leaving out the boundary value for ≤ or ≥.
  • Stopping after finding one solution.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Whole-number exponentsOrder of operationsEvaluating expressionsOne-step equationsDistributive property with numbers

FAQ

Which of 2, 4, 6, 8 are solutions of x + 3 > 7?

x + 3 > 7 means x > 4. So 6 and 8 are solutions; 4 is not, because 4 + 3 = 7 is not greater than 7.

What is the difference between x > 5 and x ≥ 5?

x ≥ 5 includes 5 itself; x > 5 does not. Both include every number bigger than 5.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix solutions to inequalities with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.