College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises - Page 164: 86


$\left( -\infty,\dfrac{2}{5} \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 7x-2(x-3)\le5(2-x) ,$ use the Distributive Property and the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} 7x-2(x)-2(-3)\le5(2)+5(-x) \\\\ 7x-2x+6\le10-5x .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 7x-2x+5x\le10-6 \\\\ 10x\le4 \\\\ x\le\dfrac{4}{10} \\\\ x\le\dfrac{2}{5} .\end{array} Hence, the solution set is the interval $ \left( -\infty,\dfrac{2}{5} \right] .$
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