#### Answer

$$x=-11\quad \mathrm{or}\quad \:x=-\frac{1}{3}$$

#### Work Step by Step

Since the value inside the absolute value can be positive or negative, we must consider both options. Doing this, we find:
$$\left|3x+17\right|=16\\ 3x+17=-16\quad \mathrm{or}\quad \:3x+17=16\\ x=-11\quad \mathrm{or}\quad \:x=-\frac{1}{3}$$