$(−\infty,−3] \cup [3,\infty)$

$(−\infty,2] \cup [6,\infty)$

Question 1

Which of the following is the correct interval notation for the solution set of the inequality $|x| > 4$?

Accepted Answer

$(−\infty,−4) \cup (4,\infty)$

Question 2

Solve the inequality $|2x-3| \leq 7$ and express the solution in interval notation.

Accepted Answer

$[−2,5]$

Question 3

Which of the following compound inequalities is equivalent to $|x+1| < 6$?

Accepted Answer

$−6 < x+1 < 6$

Question 4

What is the solution set for $|x| \geq 3$?

Accepted Answer

$(−\infty,−3] \cup [3,\infty)$

Question 5

Solve the inequality $−2(3x−2) \geq 4−x$ and give the solution in interval notation.

Accepted Answer

$(−\infty,2]$

Question 6

If $|x| < −5$, what is the solution set?

Accepted Answer

$\varnothing$ (the empty set)

Question 7

Which of the following represents the solution to $|x−4| \geq 2$?

Accepted Answer

$(−\infty,2] \cup [6,\infty)$

Question 8

Solve the compound inequality $2x−3 > 5$ and $4−x \leq 3$. Express the solution in interval notation.

Accepted Answer

$(4,7]$

Question 9

Which of the following is the correct interval notation for the solution set of $|x+2| > 5$?

Accepted Answer

$(−\infty,−7) \cup (3,\infty)$

Question 10

Given $A = (−4,6]$ and $B = [2,10)$, what is $A \cap B$?

Accepted Answer

$[2,6]$

Question 11

Solve the absolute value inequality $|3x+2| < 7$ and give the solution in interval notation.

Accepted Answer

$(−3,\frac{5}{3})$

Question 12

Which of the following is the correct solution set for $|x| \leq 8$?

Accepted Answer

$[−8,8]$

Question 13

If $|x−5| \leq 0$, what is the solution set?

Accepted Answer

$\{5\}$

Question 14

Solve the inequality $1/2(x+6) > 3$ or $4(x−1) < 3x−4$. Express the solution in interval notation.

Accepted Answer

$(0,\infty)$

Question 15

Which of the following is the correct interval notation for the solution set of $−10 < 2x−7 \leq 4$?

Accepted Answer

$(−1.5,5.5]$

Linear and Absolute Value Inequalities: Study Guide

Study Guide - Practice Questions