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

Published by Pearson

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 136: 113

Answer

$x\gt \dfrac{y-b}{a}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $y\lt ax+b$ for $x ,$ where $a\gt0.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} y\lt ax+b \\\\ -ax\lt b-y .\end{array} Since $a\gt0,$ then the inequality above is equivalent to \begin{array}{l}\require{cancel} -ax\lt b-y .\end{array} Dividing both sides by $-a$ (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -ax\lt b-y \\\\ x\gt \dfrac{b-y}{-a} \\\\ x\gt \dfrac{y-b}{a} .\end{array}

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