Question

Solve the inequality $\left|x-5\right|\le \mathbf{3}$, express the solution using interval notation and graph the solution set on real number line.

Short answer

The solution of the inequality $\left|x-5\right|\le 3$is $2\le x\le 8$whose interval notation is $x\in \left[2,8\right]$and graph is shown on real number line.

Step-by-step solution

Step 1. Solve the given inequality.

$\begin{array}{c}\left|x-5\right|\le \mathrm{3....}\left(\text{Given}\right)\\ -3\le x-5\le 3\\ x-5\ge -3\text{and}x-5\le 3\\ x\ge 2\text{and}x\le 8\end{array}$

Combining both solutions $x\ge 2\text{and}x\le 8$, the solution of the inequality is $2\le x\le 8$.

Step 2. Writing interval notation and graph of solution on real number line.

The interval notation for$2\le x\le 8$ is written as $x\in \left[2,8\right]$.

The graph of solution on real number line is shown below.

Step 3. Description of steps.

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