ACT Math Inequalities: Solve Compound Inequalities in Your Head

Compound inequalities like -2Key rule: Reverse the inequality sign only if you multiply or divide all parts by a negative number. If you add, subtract, multiply by positive, or divide by positive, the sign stays the same.

Example: If -2x<6, divide all parts by -2 (negative), which reverses the sign: x>-3. If 2x<6, divide by 2 (positive), which keeps the sign: x<3. This rule trips up many students, so burn it into memory: sign flips only with negative multiplication/division.

Mistake 1: Forgetting to reverse the sign when multiplying/dividing by a negative. This is the most common error. Always ask "Did I multiply or divide by negative?" and reverse if yes. Mistake 2: Reversing the sign when you shouldn't. If you add or subtract, never reverse. Mistake 3: Setting up a "sandwich" inequality incorrectly. For -2Always work from outside to inside when solving compound inequalities.

Create a visual reminder: write "FLIP = Negative multiplication/division" on a card and keep it at your desk this week. This reinforces the critical rule.

Problem 1: -112. Divide by -4 (negative, so flip): x<-3. Problem 5: -2≤3x-5<4. Add 5: 3≤3x<9. Divide by 3: 1≤x<3. Solve all five, showing each step and marking where you reverse (if at all) the sign.

Now find five compound inequality questions from a practice test. Solve them step-by-step, pausing after each operation to ask "Did I multiply or divide by negative?" By the fifth question, the method will feel automatic.

Compound inequalities appear on most ACT Math tests, usually in the medium-difficulty range (questions 30-45). Once you know the method, they're mechanical and fast to solve. Students who master compound inequalities pick up 1-2 points because the skill is straightforward and rewards careful execution of a predictable method.

Drill compound inequalities daily this week. Each day, solve five problems from a practice test, focusing on identifying where to reverse the sign. By test day, you should solve any compound inequality in under 60 seconds.