Answer
$-32\le x \le 8$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-2\le \dfrac{x+2}{-5} \le 6
.$ Then graph.
$\bf{\text{Solution Details:}}$
Multiplying both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2\le \dfrac{x+2}{-5} \le 6
\\\\
-5(-2)\le -5\left( \dfrac{x+2}{-5} \right) \le -5(6)
\\\\
10\ge x+2 \ge -30
.\end{array}
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
10\ge x+2 \ge -30
\\\\
10-2\ge x+2-2 \ge -30-2
\\\\
8\ge x \ge -32
\\\\
-32\le x \le 8
.\end{array}
The graph includes the points from $-32$ (inclusive) to $8$ (inclusive).
