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

$\text{Set Builder Notation: } \left\{ t|t\le-12 \right\} \\\text{Interval Notation: } \left( -\infty,-12 \right]$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $13\le-\dfrac{2}{3}t+5 .$ Write the answer in both set-builder notation and interval notation. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 13\le-\dfrac{2}{3}t+5 \\\\ 3(13)\le3\left( -\dfrac{2}{3}t+5 \right) \\\\ 39\le-2t+15 \\\\ 2t\le15-39 \\\\ 2t\le-24 \\\\ t\le-\dfrac{24}{2} \\\\ t\le-12 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ t|t\le-12 \right\} \\\text{Interval Notation: } \left( -\infty,-12 \right] .\end{array}