#### Answer

See below:

#### Work Step by Step

Consider the given inequality,
$\left| 2x+3 \right|\le 13$
Using the definition of the modulus function, we will breakdown the expression as below:
$-13\le 2x+3\le 13$
This can be further simplified as:
$\begin{align}
& -13-3\le 2x+3-3\le 13-3 \\
& -16\le 2x\le 10 \\
& \frac{-16}{2}\le \frac{2x}{2}\le \frac{10}{2} \\
& -8\le x\le 5
\end{align}$
The solution set consists of all real number greater than or equal to $-8$ and less than or equal to $5$
$\left\{ -8\le x\le 5 \right\}$