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

$\text{Set Builder Notation: } \{t|t\le -3\} \\\text{Interval Notation: } (-\infty,-3]$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $5\ge t+8 .$ Write the answer in both set-builder notation and interval notation. Finally, graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 5\ge t+8 \\\\ -t\ge 8-5 \\\\ -t\ge 3 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -t\ge 3 \\\\ \dfrac{-t}{-1}\ge \dfrac{3}{-1} \\\\ t\le -3 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{t|t\le -3\} \\\text{Interval Notation: } (-\infty,-3] .\end{array}