#### Answer

$\left[ -2,\dfrac{5}{2} \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-12 \le -6x+3 \le 15
,$ 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}
-12-3 \le -6x+3-3 \le 15-3
\\\\
-15 \le -6x \le 12
.\end{array}
Dividing all sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-15}{-6} \ge \dfrac{-6x}{-6} \ge \dfrac{12}{-6}
\\\\
\dfrac{5}{2} \ge x \ge -2
\\\\
-2 \le x \le \dfrac{5}{2}
.\end{array}
In interval notation, the solution set is $
\left[ -2,\dfrac{5}{2} \right]
.$
The red graph is the graph of the solution set.