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

$\text{Set Builder Notation: } \{x|x\le -9\} \\\text{Interval Notation: } (-\infty,-9]$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $2x\le x-9 .$ 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 equation is equivalent to \begin{array}{l}\require{cancel} 2x\le x-9 \\\\ 2x-x\le -9 \\\\ x\le -9 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{x|x\le -9\} \\\text{Interval Notation: } (-\infty,-9] .\end{array}