Answer
$\left[ -1,\dfrac{5}{2} \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-8 \le -4x+2 \le 6
,$ 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}
-8-2 \le -4x+2-2 \le 6-2
\\\\
-10 \le -4x \le 4
.\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{-10}{-4} \ge \dfrac{-4x}{-4} \ge \dfrac{4}{-4}
\\\\
\dfrac{5}{2} \ge x \ge -1
\\\\
-1\le x \le \dfrac{5}{2}
.\end{array}
In interval notation, the solution set is $
\left[ -1,\dfrac{5}{2} \right]
.$
The red graph is the graph of the solution set.