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: 81

Answer

$x=\left\{ -3,-5 \right\}$

Work Step by Step

Using the properties of equality, the given equation, $ |x+4|+1=2 ,$ is equivalent to \begin{array}{l}\require{cancel} |x+4|=2-1 \\\\ |x+4|=1 .\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} x+4=1 \text{ OR } x+4=-1 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x+4=1 \\\\ x=1-4 \\\\ x=-3 \\\\\text{ OR }\\\\ x+4=-1 \\\\ x=-1-4 \\\\ x=-5 .\end{array} Hence, the solutions are $ x=\left\{ -3,-5 \right\} .$
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