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 - Review Exercises: Chapter 2 - Page 149: 42


$\text{Set Builder Notation: } \left\{ y|y\le-4 \right\} \\\text{Interval Notation: } \left( -\infty,-4 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 7-3y\ge27+2y .$ Write the answer in both set-builder notation and interval notation. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 7-3y\ge27+2y \\\\ -3y-2y\ge27-7 \\\\ -5y\ge20 .\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} -5y\ge20 \\\\ y\le\dfrac{20}{-5} \\\\ y\le-4 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ y|y\le-4 \right\} \\\text{Interval Notation: } \left( -\infty,-4 \right] .\end{array}
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