Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 2 - Systems of Linear Equations and Inequalities - 2.5 Absolute Value Equations and Inequalities - 2.5 Exercises - Page 186: 3

Answer

$x=\{ -22,8 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of absolute value equality to solve the given equation, $ |h+7|=15 .$ Do checking of the solution/s. $\bf{\text{Solution Details:}}$ 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} h+7=15 \\\\\text{OR}\\\\ h+7=-15 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} h+7=15 \\\\ h=15-7 \\\\ h=8 \\\\\text{OR}\\\\ h+7=-15 \\\\ h=-15-7 \\\\ h=-22 .\end{array} If $h=8,$ then \begin{array}{l}\require{cancel} |h+7|=15? \\\\ |8+7|=15? \\\\ |15|=15? \\\\ 15=15 \text{ (TRUE)} .\end{array} If $h=-22,$ then \begin{array}{l}\require{cancel} |h+7|=15? \\\\ |-22+7|=15? \\\\ |-15|=15? \\\\ 15=15 \text{ (TRUE)} .\end{array} Hence, $ x=\{ -22,8 \} .$
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