Question 1

Which of the following interval notations correctly represents the solution to the inequality $a < x < b$?

Accepted Answer

$(a, b)$

Question 2

Given the compound inequality $x < -2$ or $x > 5$, which of the following is the correct interval notation for the solution set?

Accepted Answer

$(-\infty, -2) \cup (5, \infty)$

Question 3

If $|x| < 3$, which of the following is equivalent to this absolute value inequality?

Accepted Answer

$-3 < x < 3$

Question 4

Solve the inequality $-8x + 1 < 17$ and choose the correct solution interval.

Accepted Answer

$x < -2$

Question 5

Which property of inequalities allows you to add the same number to both sides of an inequality without changing its truth value?

Accepted Answer

Addition Property

Question 6

A board is to be cut to a length of 24 in. The measurement error is no more than 0.02 in. Let $x$ represent the actual length of the board. Which absolute value inequality represents the possible values of $x$?

Accepted Answer

$|x - 24| < 0.02$

Question 7

Given the inequality $4 - 3x \geq -2(x + 3) - x$, what is the solution for $x$?

Accepted Answer

$x \leq 1$

Question 8

If $|x| > 3$, which of the following describes the solution set?

Accepted Answer

$x < -3$ or $x > 3$

Question 9

A recent year’s monthly snowfall (in inches) for Chicago for November, December, January, and February was 2.8, 8.4, 11.2, and 7.9 respectively. How much snow would be necessary in March for the average monthly snowfall to exceed 7.28 inches for these five months?

Accepted Answer

$x > 6.98$

Question 10

Which of the following is the correct solution to the compound inequality $x - 6 > 1$ and $\frac{1}{2}x \geq 6$?

Accepted Answer

$x > 12$

Question 11

If $|x + 1| - 4 \leq 1$, what is the solution set for $x$?

Accepted Answer

$-2 \leq x \leq 4$

Question 12

Which of the following is the correct interval notation for the solution to $x \geq a$?

Accepted Answer

$[a, \infty)$

Question 13

Solve the inequality $8 = -\frac{5}{2}x - 2$ for $x$.

Accepted Answer

$x = -4$

Question 14

Which property of inequalities states that if $a < b$ and $b < c$, then $a < c$?

Accepted Answer

Transitive Property

Question 15

If $|2x + 7| + 5 < 1$, what is the solution set for $x$?

Accepted Answer

No solution

Question 16

Which of the following is the correct solution to $-6 \leq 5 - 3x + 9 < 0$?

Accepted Answer

$x > 2$ and $x < 6$

Question 17

If $|x| = 8$, what are the possible values of $x$?

Accepted Answer

$x = 8$ or $x = -8$

Question 18

Which of the following is the correct solution to $-2 \leq \frac{5x - 1}{3} \leq 5$?

Accepted Answer

$-1 \leq x \leq 3.6$

Question 19

If $|x + 6| \leq 8$, what is the solution set for $x$?

Accepted Answer

$-14 \leq x \leq 2$

Linear and Absolute Value Inequalities: Concepts, Properties, and Applications

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