Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Review - Page 113: 76

Answer

$x=\left\{ -\dfrac{8}{5},7 \right\}$

Work Step by Step

Using the properties of absolute value, the given equation, $ |6x+1|=|15+4x| ,$ is equivalent to \begin{array}{l}\require{cancel} 6x+1=15+4x \\\text{ and } \\ 6x+1=-(15+4x) .\end{array} Using the properties of equality, then \begin{array}{l}\require{cancel} 6x+1=15+4x \\ 6x-4x=15-1 \\ 2x=14 \\ x=\dfrac{14}{2} \\ x=7 \\\\\text{ and } \\\\ 6x+1=-(15+4x) \\ 6x+1=-15-4x \\ 6x+4x=-15-1 \\ 10x=-16 \\ x=-\dfrac{16}{10} \\ x=-\dfrac{8}{5} .\end{array} Hence, the solution set is $ x=\left\{ -\dfrac{8}{5},7 \right\} .$
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