Answer
$\left[-\frac{10}{3},-\frac{13}{6}\right]$
Refer to the attached image below for the graph.
Work Step by Step
Subtract 7 to each part to have:
$\\-3-7 \le 3x+7-7 \le \frac{1}{2}-7
\\-10 \lt 3x \le \frac{1}{2}-\frac{14}{2}
\\-10 \le x \le -\frac{13}{2}$
Divide $3$ to each part to have:
$\\\frac{-10}{3} \le x \le \dfrac{-\frac{13}{2}}{3}
\\-\frac{10}{3} \le x \le -\frac{13}{6}$
Thus, the solution is $\left[-\frac{10}{3},-\frac{13}{6}\right]$.
