## Intermediate Algebra (12th Edition)

$\left[ -\dfrac{14}{3}, 2 \right]$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-19 \le 3x-5 \le 1 ,$ use the properties of inequality. 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, the inequality above is equivalent to \begin{array}{l}\require{cancel} -19+5 \le 3x-5+5 \le 1+5 \\\\ -14 \le 3x \le 6 \\\\ -\dfrac{14}{3} \le \dfrac{3x}{3} \le \dfrac{6}{3} \\\\ -\dfrac{14}{3} \le x \le 2 .\end{array} In interval notation, the solution set is $\left[ -\dfrac{14}{3}, 2 \right] .$ The red graph is the graph of the solution set.