Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Review Exercises: 66

Answer

$x=\left\{ -\dfrac{3}{2},\dfrac{1}{2} \right\}$

Work Step by Step

Using the properties of equality, the given equation, $ |4x+2|-7=-3 ,$ is equivalent to \begin{array}{l}\require{cancel} |4x+2|=-3+7 \\\\ |4x+2|=4 .\end{array} Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the equation above is equivalent to \begin{array}{l}\require{cancel} 4x+2=4 \text{ OR } 4x+2=-4 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 4x+2=4 \\\\ 4x=4-2 \\\\ 4x=2 \\\\ x=\dfrac{2}{4} \\\\ x=\dfrac{1}{2} \\\\\text{ OR }\\\\ 4x+2=-4 \\\\ 4x=-4-2 \\\\ 4x=-6 \\\\ x=-\dfrac{6}{4} \\\\ x=-\dfrac{3}{2} .\end{array} Hence, the solutions are $ x=\left\{ -\dfrac{3}{2},\dfrac{1}{2} \right\} .$
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