Intermediate Algebra (12th Edition)

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

Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 12

Answer

$x=\{ -11,8 \}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |2x+3|=19 ,$ is equivalent to \begin{array}{l}\require{cancel} 2x+3=19 \text{ OR } 2x+3=-19 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x+3=19 \\\\ 2x=19-3 \\\\ 2x=16 \\\\ x=\dfrac{16}{2} \\\\ x=8 \\\\\text{ OR }\\\\ 2x+3=-19 \\\\ 2x=-19-3 \\\\ 2x=-22 \\\\ x=-\dfrac{22}{2} \\\\ x=-11 .\end{array} Hence, the solutions are $ x=\{ -11,8 \} .$
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