≤ Inequalities

Inequality Symbols

• < — strictly less than
• > — strictly greater than
• ≤ — less than or equal to
• ≥ — greater than or equal to

An inequality has infinitely many solutions — a range of values, not just one number.

Solving Inequalities

Use the same steps as equations — with one critical exception: when you multiply or divide both sides by a negative number, flip the inequality sign.

Example: −2x < 8 → divide by −2 and flip → x > −4.

Graphing on a Number Line

• Open circle (○) for strict inequalities (< or >) — the endpoint is NOT included
• Closed circle (●) for ≤ or ≥ — the endpoint IS included
• Shade the arrow in the direction of solutions