CMClearMathAcademy

Inequalities

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

Inequalities compare values that may not be equal. The symbols mean less than, greater than, less than or equal to, and greater than or equal to. When multiplying or dividing both sides by a negative number, the inequality direction reverses. In Algebra Readiness, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Speed limits, age restrictions, dosage ranges, and budget caps are stated as inequalities. The solution is the whole set of values that work, which is why a number-line picture is the natural way to show it.

Worked example

Problem. Solve x + 4 < 10.

  1. Subtract 4 from both sides.
  2. x < 6.
  3. The solution is every number less than 6.
  4. Connect the calculation back to Inequalities so the method, not just the arithmetic, is clear.

Answer: x < 6

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

Practice problems

1. Which phrase matches x > 8?

Choices: x is greater than 8 · x is less than 8 · x equals 8 · x is at most 8

Show solution
  1. The symbol > means greater than.

Answer: x is greater than 8

2. Solve x + 3 < 9. Enter the boundary number.

Show solution
  1. Subtract 3 from both sides.
  2. x < 6, so the boundary number is 6.

Answer: 6

3. Solve y - 5 > 12. Enter the boundary number.

Show solution
  1. Add 5 to both sides.
  2. y > 17, so the boundary number is 17.

Answer: 17

4. Which numbers satisfy x < 4?

Choices: 3 only · 4 only · 5 only · 4 and 5

Show solution
  1. Numbers less than 4 satisfy x < 4.
  2. 3 is less than 4.

Answer: 3 only

5. Solve 2x <= 14. Enter the boundary number.

Show solution
  1. Divide both sides by 2.
  2. x <= 7.

Answer: 7

Practice this interactively with instant feedback and an AI tutor.

Practice Inequalities Take the free placement check

More Pre-Algebra lessons