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 - Page 119: 60

Answer

$x=\{ 2,4 \}$
1512972980

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |9-3x|=3 ,$ use the definition of absolute value equality. 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 equation above is equivalent to \begin{array}{l}\require{cancel} 9-3x=3 \\\\\text{OR}\\\\ 9-3x=-3 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 9-3x=3 \\\\ -3x=3-9 \\\\ -3x=-6 \\\\ x=\dfrac{-6}{-3} \\\\ x=2 \\\\\text{OR}\\\\ 9-3x=-3 \\\\ -3x=-3-9 \\\\ -3x=-12 \\\\ x=\dfrac{-12}{-3} \\\\ x=4 .\end{array} Hence, $ x=\{ 2,4 \} .$ The colored points is the graph of the solution set.
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