Chapter A.9, Problem 97AYU

To determine

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

Answer to Problem 97AYU

$\left\{x|-1 \le x \le 1\right\}\text{ or }\left[-1, 1\right]$

Explanation of Solution

$\begin{array}{l}|-4x| + |-5| \le 9\hfill \\ |-4x| + 5 \le 9\hfill \\ |-4x| + 5 - 5 \le 9-5\hfill \\ |-4x| \le 4\hfill \\ -4 \le -4x \le 4\hfill \end{array}$

Divide by $-4$

$\begin{array}{c}1 \ge x \ge -1\\ -1 \le x \le 1\end{array}$

The solution set is $\left\{x|-1 \le x \le 1\right\}$ or using interval notation, all numbers in the interval $\left[-1, 1\right].$