ACT Math inequalities use the same inverse operations as equations, but flip the sign when you multiply or divide by a negative number—and graph solutions on a number line with open or closed circles. They appear inside algebra and word-problem setups throughout the section.
Solving linear inequalities
Isolate the variable like a linear equation. When you multiply or divide both sides by a negative, reverse the inequality symbol. Example: -2x > 6 → x < -3. Review linear equations on the ACT first—part of how much algebra is on the ACT.
Compound inequalities
-3 < 2x + 1 < 9: operate on all three parts at once, or split into two inequalities. The solution is the overlap (AND) unless the question asks for OR.
Graphing on a number line
- < or >: open circle
- ≤ or ≥: closed circle
- Shade the direction that includes your test values
Word problems
Translate phrases: "at most" → ≤, "at least" → ≥, "no more than" → ≤. Check with a number from your solution set. For systems, see systems of equations.
Start practicing
Start with a free diagnostic, then drill your weak spots with 15-question quizzes and track how you're doing across Reading, English, and Math. Compare plans whenever you're ready to go further.
This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.