Quiz about Solving absolute value equations and inequalities

Question 1

Solve for x in the following absolute value equation.

$$\left|\ \frac{x}{4}\right|\ =\ 8$$

Accepted Answer

$$\left\{\ 32,\ -32\ \right\}$$

Answer

$$\left\{\ 2,\ -2\ \right\}$$

Answer

$$\left\{\ \frac{1}{2}\ ,\ -\frac{1}{2}\right\}$$

Answer

$$\left\{\ 12,\ -12\ \right\}$$

Question 2

Solve for n in the following absolute value equation.

$$\left|\ n\ -\ 6\ \right|\ =\ -6$$

Accepted Answer

No solution

Answer

Answer

$$\left\{\ 12,\ -12\ \right\}$$

Answer

$$\left\{\ 1,\ -1\ \right\}$$

Question 3

Solve for y in the following absolute value equation.

$$\left|\ 2y\ -\ 4\ \right|\ =\ 0\ $$

Accepted Answer

Answer

$$\left\{\ 4,\ -4\ \right\}$$

Answer

$$\left\{\ 2,\ -2\ \right\}$$

Answer

$$\left\{\ 8,\ -8\ \right\}$$

Question 4

Solve for b in the following equation.

$$\left|\ \frac{b}{3}\ +\ 3\ \right|\ =\ 9$$

Accepted Answer

$$\left\{\ 18,\ -36\ \right\}$$

Answer

$$\left\{\ 2,\ 4\ \right\}$$

Answer

$$\left\{\ 2,\ -4\ \right\}$$

Answer

$$\left\{\ 18,\ 36\ \right\}$$

Question 5

Solve for x in the following absolute value inequality.

$$\left|\ 8x\ +4\ \right|\ >12$$

Accepted Answer

$$x\ >\ 1\ or\ x\ <\ -2$$

Answer

$$x\ <\ 1\ and\ x\ >\ -2$$

Answer

$$x\ >\ -1\ and\ x\ <\ 2$$

Answer

$$x\ <\ -1\ or\ x\ >\ 2$$

Question 6

Solve for the value of m in the following absolute value inequality.

$$\left|\ \frac{m}{5}\ -\ 1\ \right|\ \ \le\ \ 19$$

Accepted Answer

$$m\ \le\ 100\ \ AND\ \ m\ \ge\ -90$$

Answer

$$m\ \le\ 4\ \ AND\ \ m\ \ge\ -\frac{18}{5}$$

Answer

$$m\ \ge\ 4\ \ OR\ \ m\ \ge\ -\frac{18}{5}$$

Answer

$$m\ \ge\ 100\ \ OR\ \ m\ \le\ -90$$

Question 7

Solve for the value of y in the following absolute value inequality.

$$\left|\ y\ \right|\ -\ 8\ \ge\ 12$$

Accepted Answer

$$y\ \ge\ 20\ \ OR\ \ y\ \le\ -20$$

Answer

$$y\ \ge\ 20\ \ OR\ \ y\ \le\ -4$$

Answer

$$y\ \ge\ 20\ \ AND\ \ y\ \le\ -20$$

Answer

$$y\ \ge\ 20\ \ AND\ \ y\ \le\ -4$$

Question 8

Solve for the value of b in the following inequality.

$$\left|\ 3b\ +\ 7\ \right|\ -\ 6\ <\ 1$$

Accepted Answer

$$b\ \ <\ \ 0\ \ AND\ \ b\ \ >\ \ -\frac{14}{3}$$

Answer

$$b\ \ <\ \ 0\ \ OR\ \ b\ \ >\ \ -\frac{2}{3}$$

Answer

$$b\ \ <\ \ 0\ \ AND\ \ b\ \ >\ \ -\frac{2}{3}$$

Answer

$$b\ \ <\ \ 0\ \ OR\ \ b\ \ >\ \ -\frac{14}{3}$$

Solving absolute value equations and inequalities

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