College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.8 - Solving Absolute Value Equations and Inequalities - 1.8 Exercises - Page 153: 20


$\displaystyle x=\frac{25}{6}$ $\displaystyle x=-\frac{65}{6}$

Work Step by Step

$|\displaystyle \frac{3}{5}x+2|-\frac{1}{2}=4$ $|\frac{3}{5}x+2|=4+\frac{1}{2}=\frac{9}{2}$ We split the absolute value into two equations, the positive and negative: $\displaystyle \frac{3}{5}x+2=\frac{9}{2}$ $\displaystyle \frac{3}{5}x=\frac{5}{2}$ $\displaystyle x=\frac{25}{6}$ $\displaystyle \frac{3}{5}x+2=-\frac{9}{2}$ $\displaystyle \frac{3}{5}x=-\frac{13}{2}$ $\displaystyle x=-\frac{65}{6}$
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