ACT-Style: Inequality Solving

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Inequality Solving The #1 inequality trap on the ACT: what happens to the sign when you divide by a negative Which of the following represents all values of x that satisfy the inequality ? Nice work — you solved a linear inequality that requires the single most commonly-tested rule on the ACT: flipping the sign when you multiply or divide by a negative number. Solve inequalities like equations, with ONE exception: add/subtract the same value from both sides exactly as you would in an equation — that part never changes the sign. Flip the sign when you multiply or divide by a NEGATIVE: dividing by -5 flips to , giving (choice E). Skipping this flip is the #1 ACT trap and produces choice D, — correct arithmetic, wrong direction. Watch the direction you move the constant: subtracting 8 from both sides of gives . Adding 8 instead (a sign slip on which way the constant moves) gives , which flips to choice C, . A negative divided by a negative is positive: , not -4 . Miscomputing that quotient's sign — even after correctly flipping the inequality — lands on choice A ( ) or, combined with also forgetting to flip, choice B ( ). Any time you divide or multiply an ACT inequality by a negative number, say the flip out loud before you move on — it's the single easiest point to lose on an otherwise easy question.

This is the written version of the interactive lesson above. See the full ACT Math course.