## College Algebra (11th Edition)

$\left( -\dfrac{7}{3},-1 \right)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-8\gt3x-5\gt-12 ,$ use the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -8+5\gt3x-5+5\gt-12+5 \\\\ -3\gt3x\gt-7 \\\\ \dfrac{-3}{3}\gt\dfrac{3x}{3}\gt-\dfrac{7}{3} \\\\ -1\gt x\gt-\dfrac{7}{3} \\\\ -\dfrac{7}{3}\lt x\lt -1 .\end{array} Hence, the solution set is the interval $\left( -\dfrac{7}{3},-1 \right) .$