College Algebra (11th Edition)

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

Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises: 18


$x= \left\{ \dfrac{1}{5}, 7 \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the solution/s to the given equation, $ \left| \dfrac{2x+3}{3x-4} \right|=1 ,$ is/are \begin{array}{l}\require{cancel} \dfrac{2x+3}{3x-4}=1 \\\\ 2x+3=1(3x-4) \\\\ 2x+3=3x-4 \\\\ 2x-3x=-4-3 \\\\ -x=-7 \\\\ x=7 \\\\\text{OR}\\\\ \dfrac{2x+3}{3x-4}=-1 \\\\ 2x+3=-1(3x-4) \\\\ 2x+3=-3x+4 \\\\ 2x+3x=4-3 \\\\ 5x=1 \\\\ x=\dfrac{1}{5} .\end{array} Hence, the solutions are $ x= \left\{ \dfrac{1}{5}, 7 \right\} .$
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