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Inequalities (linear and compound) — ACT practice questions

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

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

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

A$-2<x\leq4$✓ CorrectB$-2\leq x<4$✗ Not this oneC$-1<x\leq5$✗ Not this oneD$-6<x\leq12$✗ Not this one

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Answer: A — $-2<x\leq4$

Subtracting 1 gives $-6<3x\leq12$. Dividing all three parts by 3 gives $-2<x\leq4$.

Question 2Easier

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

A$|m-50|\le3$✓ CorrectB$|m-3|\le50$✗ Not this oneC$|m-50|\ge3$✗ Not this oneD$|m+50|<3$✗ Not this one

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Answer: A — $|m-50|\le3$

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

Question 3Mid

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?

A12✗ Not this oneB13✗ Not this oneC14✓ CorrectD15✗ Not this one

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Answer: C — 14

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

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