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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 135: 64


$\text{Set Builder Notation: } \left\{ a|a\le-3.6 \right\} \\\text{Interval Notation: } \left(-\infty,-3.6 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 9\le-2.5a .$ 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} 9\le-2.5a \\\\ 2.5a\le-9 \\\\ 10(2.5a)\le10(-9) \\\\ 25a\le-90 \\\\ a\le-\dfrac{90}{25} \\\\ a\le-\dfrac{18}{5} \\\\ a\le-3.6 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ a|a\le-3.6 \right\} \\\text{Interval Notation: } \left(-\infty,-3.6 \right] .\end{array}
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