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Worksheets›Algebra 1›Equations & inequalities›Compound inequalities

Compound 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.

Algebra 1CCSS HSA.REI.B.3Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Three-part inequalities

  1. 1.−13 ≤ x − 7 < −9
  2. 2.−7 < x + 1 ≤ −2
  3. 3.3 ≤ x + 2 ≤ 8
  4. 4.−8 < x − 6 ≤ −2
  5. 5.−10 ≤ x − 8 ≤ −2
  6. 6.−5 < x − 3 < 0
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

For a three-part inequality, do the same thing to all three parts. An absolute value less than a number becomes a three-part inequality; greater than a number becomes two separate inequalities joined by or.

Easy8 ≤ x + 8 ≤ 17Three-part inequalitiesMediumx − 9 ≤ 0 or x − 9 ≥ 9With a coefficient, and or-inequalitiesHard|2x − 8| > 10Absolute value inequalities

How to solve it: a worked example

Solve each inequality. Write the answer as a compound inequality.

  1. Start−4 ≤ x − 2 < 5
  2. Add 2 to all three parts−2 ≤ x < 7
  3. Answer−2 ≤ x < 7

Common mistakes to watch for

  • Doing the step to only the middle part of a three-part inequality.
  • Forgetting to flip both signs when dividing by a negative.
  • Writing |x| > 3 as −3 < x < 3: greater than gives two pieces joined by or.

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

Related worksheets

Multi-step inequalitiesAbsolute value equationsLiteral equationsSlope-intercept formParallel and perpendicular lines

FAQ

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 compound 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.