Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set: 26

Answer

$x=\left\{ -8,14 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |x-3|=11 ,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to \begin{array}{l}\require{cancel} x-3=11 \\\\\text{OR}\\\\ x-3=-11 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x-3=11 \\\\ x=11+3 \\\\ x=14 \\\\\text{OR}\\\\ x-3=-11 \\\\ x=-11+3 \\\\ x=-8 .\end{array} Hence, $ x=\left\{ -8,14 \right\} .$
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