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

$\text{Set Builder Notation: } \{ n|n\lt0 \} \\\text{Interval Notation: } (-\infty,0)$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $-8n+12\gt12-7n .$ 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} -8n+12\gt12-7n \\\\ -8n+7n\gt12-12 \\\\ -n\gt0 .\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} -n\gt0 \\\\ \dfrac{-n}{-1}\gt\dfrac{0}{-1} \\\\ n\lt0 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{ n|n\lt0 \} \\\text{Interval Notation: } (-\infty,0) .\end{array}