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: 80

Answer

$\left(-\infty,2 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 7-8y\gt5-7y .$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 7-8y\gt5-7y \\\\ -8y+7y\gt5-7 \\\\ -y\gt-2 .\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} -y\gt-2 \\\\ \dfrac{-y}{-1}\gt\dfrac{-2}{-1} \\\\ y\lt2 .\end{array} Hence, the solution set is $ \left(-\infty,2 \right) .$
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