Question

Solve the absolute inequality. Express the answer using interval notation and graph the solution set.

$\left|16x\right|\le 8$

Short answer

The answer is$-\frac{1}{2}\le x\le \frac{1}{2}$.

The interval notation of the solution is$\left[-\frac{1}{2},\frac{1}{2}\right]$.

The graph of the solution set $-\frac{1}{2}\le x\le \frac{1}{2}$.

Step-by-step solution

Step 1. Solve the absolute value inequality.

$\begin{array}{c}\left|16x\right|\le 8\\ -8\le 16x\le 8\\ -\frac{1}{2}\le x\le \frac{1}{2}\end{array}$

Hence, the solution set is $-\frac{1}{2}\le x\le \frac{1}{2}$.

Step 2. Express the interval notation of the solution set.

The interval notation of the solution set $-\frac{1}{2}\le x\le \frac{1}{2}$is $\left[-\frac{1}{2},\frac{1}{2}\right]$.

Step 3. Graph the solution set.

The graph of the solution set $-\frac{1}{2}\le x\le \frac{1}{2}$.