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Linear Inequalities

A free Algebra I lesson from the “Algebra Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Solving linear inequalities is similar to solving equations, but the result is a range of values. If you multiply or divide both sides by a negative number, reverse the inequality symbol. In Algebra Foundations, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Inequalities model limits such as budget caps, minimum scores, speed ranges, inventory thresholds, and safety tolerances.

Worked example

Problem. Solve -2x + 5 < 13.

  1. Subtract 5 from both sides: -2x < 8.
  2. Divide by -2 and flip the inequality.
  3. x > -4.
  4. Connect the result back to Linear Inequalities so the method and meaning are both clear.

Answer: x > -4

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Solve x + 6 > 14. Enter the boundary number.

Show solution
  1. Subtract 6 from both sides.
  2. x > 8.

Answer: 8

2. Solve 3x <= 21. Enter the boundary number.

Show solution
  1. Divide by 3.
  2. x <= 7.

Answer: 7

3. Which phrase matches x >= -2?

Choices: x is at least -2 · x is below -2 · x is less than -2 · x equals -2 only

Show solution
  1. Greater than or equal to means at least.

Answer: x is at least -2

4. Solve 2x - 5 < 11. Enter the boundary number.

Show solution
  1. Add 5: 2x < 16.
  2. Divide by 2: x < 8.

Answer: 8

5. Solve -4x >= 20. Enter the boundary number.

Show solution
  1. Divide by -4 and flip the sign.
  2. x <= -5, so the boundary is -5.

Answer: -5

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