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

$\text{Set Builder Notation: } \left\{ x|x\le-\dfrac{1}{10} \right\} \\\text{Interval Notation: } \left( -\infty,-\dfrac{1}{10} \right]$ $\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $-2x\ge\dfrac{1}{5} .$ 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} -2x\ge\dfrac{1}{5} \\\\ x\le\dfrac{\dfrac{1}{5}}{-2} \\\\ x\le\dfrac{1}{5}\div-2 \\\\ x\le\dfrac{1}{5}\cdot\left(-\dfrac{1}{2} \right) \\\\ x\le-\dfrac{1}{10} .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ x|x\le-\dfrac{1}{10} \right\} \\\text{Interval Notation: } \left( -\infty,-\dfrac{1}{10} \right] .\end{array}