Intermediate Algebra (12th Edition)

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

Chapter 1 - Review Exercises: 65


$x=\left\{ 0,7 \right\} $

Work Step by Step

Using the properties of equality, the given equation, $ |2x-7|+4=11 ,$ is equivalent to \begin{array}{l}\require{cancel} |2x-7|=11-4 \\\\ |2x-7|=7 .\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} 2x-7=7 \text{ OR } 2x-7=-7 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x-7=7 \\\\ 2x=7+7 \\\\ 2x=14 \\\\ x=\dfrac{14}{2} \\\\ x=7 \\\\\text{ OR }\\\\ 2x-7=-7 \\\\ 2x=-7+7 \\\\ 2x=0 \\\\ x=\dfrac{0}{2} \\\\ x=0 .\end{array} Hence, the solutions are $ x=\left\{ 0,7 \right\} .$
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