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: 75

Answer

$x=\left\{ 3,9 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 3|x-6|=9 ,$ use the properties of equality to isolate the absolute value expression. Then use the definition of absolute value equality. Use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of equality to isolate the absolute value expression results to \begin{array}{l}\require{cancel} |x-6|=\dfrac{9}{3} \\\\ |x-6|=3 .\end{array} Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x-6=3 \\\\\text{OR}\\\\ x-6=-3 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x-6=3 \\\\ x=3+6 \\\\ x=9 \\\\\text{OR}\\\\ x-6=-3 \\\\ x=-3+6 \\\\ x=3 .\end{array} Hence, $ x=\left\{ 3,9 \right\} .$
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