## Intermediate Algebra (12th Edition)

$\left[ -3,3 \right]$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-6 \le \dfrac{4}{3}x-2 \le 2 ,$ use the properties of inequality to isolate the variable. 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 to isolate the variable results to \begin{array}{l}\require{cancel} 3(-6) \le 3\left( \dfrac{4}{3}x-2 \right) \le 3(2) \\\\ -18 \le 4x-6 \le 6 \\\\ -18+6 \le 4x-6+6 \le 6+6 \\\\ -12 \le 4x \le 12 \\\\ \dfrac{-12}{4} \le \dfrac{4x}{4} \le \dfrac{12}{4} \\\\ -3 \le x \le 3 .\end{array} In interval notation, the solution set is $\left[ -3,3 \right] .$ The colored graph is the graph of the solution set.