## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-32\le x \le 8$
$\bf{\text{Solution Outline:}}$ 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).