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Worksheets›Algebra 1›Equations & inequalities›Multi-step inequalities

Multi-Step 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: Distribute, then solve

  1. 1.3(x + 2) < 0
  2. 2.4(x + 7) ≥ 8
  3. 3.4(x + 3) ≥ 40
  4. 4.6(x − 7) ≥ −72
  5. 5.5(x − 8) < −5
  6. 6.3(x + 3) ≤ 30
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Simplify each side, collect the x-terms on one side and the numbers on the other, then divide. Dividing or multiplying by a negative number reverses the inequality.

Easy2(x + 6) > 10Distribute, then solveMedium−5x + 12 ≤ −4x + 15Variables on both sidesHard−2(x − 1) < 3x + 12Distribute with variables on both sides

How to solve it: a worked example

Solve each inequality.

  1. Start4(x − 4) ≥ −8
  2. Distribute4x − 16 ≥ −8
  3. Add 16 on both sides4x ≥ 8
  4. Divide by 4x ≥ 2
  5. Answerx ≥ 2

Common mistakes to watch for

  • Forgetting to flip the sign after dividing by a negative coefficient.
  • Flipping the sign when moving a term across, which never changes the direction.
  • Distributing to only the first term in the parentheses.

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

Related worksheets

Absolute value equationsLiteral equationsCompound inequalitiesSlope-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 multi-step 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.