Chapter A.9, Problem 98AYU

To determine

To solve: Each inequality. Express your answer using set notation or interval notation. Graph the solution set.

Answer to Problem 98AYU

$\left\{x|-6 \le x \le 6\right\}\text{ or }\left[-6, 6\right]$

Explanation of Solution

$\begin{array}{l}|-x|-4| \le 2\hfill \\ |-x|-4 + 4 \le 2 + 4\hfill \\ |-x| \le 6\hfill \\ -6 \le -x \le 6\hfill \end{array}$

Divide by $-1$

$\begin{array}{c}6 \ge x \ge -6\\ -6 \le x \le 6\end{array}$

The solution set is $\left\{x|-6 \le x \le 6\right\}$ or using interval notation, all numbers in the interval $\left[-6, 6\right].$