Answer
$\left[-\dfrac{10}{3}, -\dfrac{13}{6}\right]$
Refer to the image below for the graph.
Work Step by Step
Subtract $7$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&-3-7 &\le &3x+7-7 &\le &\frac{1}{2}-7
\\&-10 &\le &3x &\le &\frac{1}{2}-\frac{14}{2}
\\&-10 &\le &3x &\le &-\frac{13}{2}
\end{array}$
Divide $3$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&\dfrac{-10}{3} &\le &\dfrac{3x}{3} &\le &\dfrac{-\frac{13}{2}}{3}
\\&-\dfrac{10}{3} &\le &x &\le &-\dfrac{13}{6}
\end{array}$
Thus, the solution set is $\bf\left[-\dfrac{10}{3}, -\dfrac{13}{6}\right]$.
To graph this solution set, plot solid dots at $-\dfrac{10}{3}$ and $-\dfrac{13}{6}$ then shade the region in between.
(refer to the attached image in the answer part above for the graph)