Strategy #9: Solve Linear Inequalities Carefully

Category: Algebra

Solve inequalities like equations, with one critical rule: flip the inequality sign when you multiply or divide by a negative number.

Why it matters: Forgetting to flip the sign is an extremely common error. The SAT exploits this.

Example: −2x > 8 → divide both sides by −2 → x < −4 (sign flips!)

Graphing on a number line:

• Strict inequality (< or >) → open circle

• Non-strict (≤ or ≥) → closed (filled) circle

Practice tip: Before finalizing, ask yourself: "Did I multiply or divide by a negative at any step?" If yes, double-check that you flipped the sign.