Solving inequalities

Math

Definition

The process of finding all values of a variable that make an inequality true. The steps are similar to solving equations, but you must reverse the inequality sign when multiplying or dividing by a negative number.

How It Works

  1. Simplify both sides of the inequality.
  2. Use inverse operations to isolate the variable.
  3. If you multiply or divide by a negative number, flip the inequality sign.
  4. Write the solution in interval notation or graph it on a number line.

Examples

  • −3x > 12 → x < −4 (dividing by −3 flips the sign)
  • 2x + 5 ≤ 11 → 2x ≤ 6 → x ≤ 3
Key Fact

Flip the inequality sign when multiplying or dividing by a negative number.

Related Terms

Compound inequalities Graphing inequalities Absolute value equations Writing inequalities

Study This Concept

Practice solving inequalities with free review games in these units:

Pre-Algebra Unit 7: Inequalities