Answer
$18\le x \le 24$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-10\le \dfrac{x+6}{-3} \le -8
.$ 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}
-10\le \dfrac{x+6}{-3} \le -8
\\\\
-3(-10)\le -3\left( \dfrac{x+6}{-3} \right) \le -3(-8)
\\\\
30\ge x+6 \ge 24
.\end{array}
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
30\ge x+6 \ge 24
\\\\
30-6\ge x+6-6 \ge 24-6
\\\\
24\ge x \ge 18
\\\\
18\le x \le 24
.\end{array}
The graph includes the points from $18$ (inclusive) to $24$ (inclusive).
