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

$\text{Set Builder Notation: } \{ x|x\gt4 \} \\\text{Interval Notation: } (4,\infty)$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $-16x\lt-64 .$ 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 $\ge.$ $\bf{\text{Solution Details:}}$ Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -16x\lt-64 \\\\ x\gt\dfrac{-64}{-16} \\\\ x\gt4 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{ x|x\gt4 \} \\\text{Interval Notation: } (4,\infty) .\end{array}