Question

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

$\left|x-5\right|\le 3$

Short answer

The answer is$2\le x\le 8.$

The interval notation of the answer is $\left[2,8\right]$.

The graph of the solution set$2\le x\le 8.$

Step-by-step solution

Step 1. Solve the absolute value inequalities.

$\begin{array}{c}\left|x-5\right|\le 3\\ -3\le x-5\le 3\\ 2\le x\le 8\end{array}$

Hence, the solution set is$2\le x\le 8.$

Step 2. Express the solution set in interval notation.

The interval notation of the solution set $2\le x\le 8$ is $\left[2,8\right]$.

Step 3. Graph of solution set.

The graph of the solution set $2\le x\le 8.$