What is a linear inequality?

A linear inequality compares expressions using:
< > ≤ ≥

Examples:

• x + 2 > 5

• 3x ≤ 9

Solving linear inequalities

Steps are similar to equations, with one special rule:

IMPORTANT RULE:
If you multiply or divide by a negative number, you flip the inequality sign.

Example 1

Solve: x − 4 > 1

Add 4 to both sides:
x > 5

Example 2 (sign flips)

Solve: −2x ≤ 6

Divide by −2 and flip the sign:
x ≥ −3

Graphing inequalities

• Open circle: < or >

• Closed circle: ≤ or ≥

• Shade in the direction of the solution