#### Answer

$\left[ -\dfrac{14}{3}, 2 \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-19 \le 3x-5 \le 1
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-19+5 \le 3x-5+5 \le 1+5
\\\\
-14 \le 3x \le 6
\\\\
-\dfrac{14}{3} \le \dfrac{3x}{3} \le \dfrac{6}{3}
\\\\
-\dfrac{14}{3} \le x \le 2
.\end{array}
In interval notation, the solution set is $
\left[ -\dfrac{14}{3}, 2 \right]
.$
The red graph is the graph of the solution set.