#### Answer

$\left[\frac{1}{3}, 5\right]$
Refer to the image below for the graph.

#### Work Step by Step

Add $7$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&-6+7 &\le &3x-7+7 &\le &8+7
\\&1 &\le &3x &\le &15
\end{array}$
Divide $3$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&\dfrac{1}{3} &\le &\dfrac{3x}{3} &\le &\dfrac{15}{3}
\\&\dfrac{1}{3} &\le &x &\le &5
\end{array}$
Thus, the solution set is $\bf[\frac{1}{3}, 5]$.
To graph this solution set, plot solid dots at $\dfrac{1}{3}$ and $5$ then shade the region in between.
(refer to the attached image in the answer part above for the graph)