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: 19


$x=\displaystyle \frac{35}{2}$ $x=\displaystyle -\frac{25}{2}$

Work Step by Step

$\displaystyle 8+5| \frac{1}{3}x-\frac{5}{6}|=33$ $\displaystyle 5|\frac{1}{3}x-\frac{5}{6}|=33-8=25$ $\displaystyle |\frac{1}{3}x-\frac{5}{6}|=25/5=5$ We split the absolute value equation into the positive and negative: $\displaystyle \frac{1}{3}x-\frac{5}{6}=5$ $\displaystyle \frac{1}{3}x=\frac{5*6}{6}+\frac{5}{6}=\frac{35}{6}$ $x=\displaystyle \frac{35*3}{6}=\frac{35}{2}$ $\displaystyle \frac{1}{3}x-\frac{5}{6}=-5$ $\displaystyle \frac{1}{3}x=-\frac{5*6}{6}+\frac{5}{6}=-\frac{25}{6}$ $\displaystyle x=-\frac{25*3}{6}=-\frac{25}{2}$
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