Study on the flyACT

Study on the fly›ACT›Mathematics › Inequalities (linear and compound)

MathematicsFree

Inequalities (linear and compound) — ACT practice questions

Inequalities (linear and compound) on the ACT Mathematics test covers linear inequalities, compound statements with and or or, and absolute-value ranges on the real line. A student must isolate the variable, reverse the inequality when multiplying or dividing by a negative, and tell inclusive bounds from exclusive ones. Questions typically ask which inequality matches a verbal condition, which set is the solution, or which step in a growing pattern first exceeds a stated limit. The five answer choices usually look alike, swapping at most with at least, mixing open and closed endpoints, or reversing the inequality sign.

  • Section: Mathematics 45 questions on the paper
  • 46 practice questions in the app

Sample questions

Question 1

Which of the following is the solution of −5<3x+1≤13-5<3x+1\leq13?

  1. A−2<x≤4-2<x\leq4
  2. B−2≤x<4-2\leq x<4
  3. C−1<x≤5-1<x\leq5
  4. D−6<x≤12-6<x\leq12
Show answer

Answer: A — −2<x≤4-2<x\leq4

Subtracting 1 gives −6<3x≤12-6<3x\leq12. Dividing all three parts by 3 gives −2<x≤4-2<x\leq4.

Question 2

Which of the following inequalities represents all real numbers mm whose distance from 50 is at most 3?

  1. A∣m−50∣≤3|m-50|\le3
  2. B∣m−3∣≤50|m-3|\le50
  3. C∣m−50∣≥3|m-50|\ge3
  4. D∣m+50∣<3|m+50|<3
Show answer

Answer: A — ∣m−50∣≤3|m-50|\le3

The expression ∣m−50∣|m-50| is the distance from mm to 50. Requiring that distance to be at most 3 gives ∣m−50∣≤3|m-50|\le3.

Question 3

A collector's display case holds 12 coins in its first row. Each row after that holds 7 more coins than the row before it. Which row is the first to contain more than 100 coins?

  1. A12
  2. B13
  3. C14
  4. D15
Show answer

Answer: C — 14

Row nn holds 12+7(n−1)12+7(n-1) coins. Row 13 holds 12+7(12)=9612+7(12)=96 coins, and row 14 holds 12+7(13)=10312+7(13)=103 coins, the first total exceeding 100.

Practice 46 Inequalities (linear and compound) questions in the app

More ACT topics

Mathematics

Everything on the ACT

Study on the fly is an independent study tool and is not affiliated with, sponsored by, or endorsed by any testing organization, school, or government body.

ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, and does not endorse, this product.

All practice questions and passages are original works created for Study on the fly and are not reproduced from any official test.