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: 63


$\text{Set Builder Notation: } \left\{ n|n\ge-1.5 \right\} \\\text{Interval Notation: } \left[ -1.5,\infty \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 1.8\ge-1.2n .$ 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} 1.8\ge-1.2n \\\\ 1.2n\ge-1.8 \\\\ 10(1.2n)\ge10(-1.8) \\\\ 12n\ge-18 \\\\ n\ge-\dfrac{18}{12} \\\\ n\ge-\dfrac{3}{2} \\\\ n\ge-1.5 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ n|n\ge-1.5 \right\} \\\text{Interval Notation: } \left[ -1.5,\infty \right) .\end{array}
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