Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 1-2 - Cumulative Review - Page 218: 33

Answer

$x\lt4$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 6x+20\gt15x-16 ,$ use the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 6x+20\gt15x-16 \\\\ 6x-15x\gt-16-20 \\\\ -9x\gt-36 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol) results to \begin{array}{l}\require{cancel} -9x\gt-36 \\\\ \dfrac{-9x}{-9}\lt\dfrac{-36}{-9} \\\\ x\lt4 .\end{array} Upon checking, any value of the variable in the solution set satisfies the original inequality. Any value of the variable not in the solution set does not satisfy the original inequality. Hence, the solution set is $ x\lt4 .$
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