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

$\text{Set Builder Notation: } \left\{ t|t\le-2 \right\} \\\text{Interval Notation: } \left( -\infty,-2 \right]$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $4t+10\le2 .$ 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} 4t+10\le2 \\\\ 4t\le2-10 \\\\ 4t\le-8 \\\\ t\le-\dfrac{8}{4} \\\\ t\le-2 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ t|t\le-2 \right\} \\\text{Interval Notation: } \left( -\infty,-2 \right] .\end{array}