## Precalculus (6th Edition) Blitzer

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 $5$ $\left\{ -8\le x\le 5 \right\}$