Question 1

Which of the following best describes the graph of $y = |f(x)|$ compared to $y = f(x)$?

Accepted Answer

It is a reflection of the portion of $y = f(x)$ below the x-axis across the x-axis.

Question 2

Solve the equation $\left| \frac{1}{2}x + 1 \right| = 5$.

Accepted Answer

$x = 8$ and $x = -12$

Question 3

Which of the following absolute value equations has no solution?

Accepted Answer

$|5 + 3x| = -4$

Question 4

Solve the equation $|1 - 2x| - 3 = -1$.

Accepted Answer

$x = -\frac{1}{2}$ and $x = \frac{3}{2}$

Question 5

A cylindrical can must have a diameter $D$ such that $|D - 3| \leq 0.02$. What is the range of acceptable values for $D$?

Accepted Answer

$2.98 \leq D \leq 3.02$

Question 6

Solve the equation $|4 - 2x| = 8$.

Accepted Answer

$x = -2$ and $x = 6$

Question 7

Which of the following is the correct solution set for $|4 - x| < 2$?

Accepted Answer

$2 < x < 6$

Question 8

Solve the inequality $|3x + 2| > 1$.

Accepted Answer

$x < -1$ or $x > -\frac{1}{3}$

Question 9

A phone's thickness $A$ must not vary from $9.33$ mm by more than $0.02$ mm. Which absolute value inequality models this requirement?

Accepted Answer

$|A - 9.33| < 0.02$

Question 10

Solve the inequality $|3 - 2x| < 5$ and express the solution in interval notation.

Accepted Answer

$(-1, 4)$

Question 11

Which of the following statements is true about the solution to $|x| = a$ where $a > 0$?

Accepted Answer

The solution is $x = a$ or $x = -a$

Question 12

Solve the equation $|2x - 5| = |1 + x|$.

Accepted Answer

$x = 6$ and $x = 4/3$

Question 13

Which of the following is the correct solution set for $|-3x + 1| > 8$?

Accepted Answer

$x < -\frac{7}{3}$ or $x > 3$

Question 14

If $|x - 4| = 0$, what is the value of $x$?

Accepted Answer

$x = 4$

Question 15

A quality control engineer needs the length $L$ of a part to be within $0.05$ units of $10$ units. Which interval describes the acceptable values for $L$?

Accepted Answer

$9.95 \leq L \leq 10.05$

Question 16

Which of the following is the correct way to solve $|ax + b| = c$ for $c > 0$?

Accepted Answer

Set $ax + b = c$ or $ax + b = -c$ and solve both equations.

Question 17

If $|x - 2| < 5$, which of the following is the equivalent compound inequality?

Accepted Answer

$-3 < x < 7$

Question 18

A machine part must be manufactured so that its width $W$ is no more than $0.01$ units away from $5$ units. Which absolute value inequality models this requirement?

Accepted Answer

$|W - 5| \leq 0.01$

Question 19

Which of the following is the solution set for $|x + 3| > 7$?

Accepted Answer

$x < -10$ or $x > 4$

Absolute Value Equations and Inequalities (Chapter 2.5) – College Algebra Study Notes

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