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 2 - Equations, Inequalities, and Problem Solving - Review Exercises: Chapter 2 - Page 150: 62


$n=\{ -23,23 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 2|n|+4=50 ,$ isolate first the absolute value expression. Then, use the definition of an absolute value equality to solve for the variable. $\bf{\text{Solution Details:}}$ Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} 2|n|+4=50 \\\\ 2|n|=50-4 \\\\ 2|n|=46 \\\\ |n|=\dfrac{46}{2} \\\\ |n|=23 .\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} n=23 \\\\\text{OR}\\\\ n=-23 .\end{array} Hence, $ n=\{ -23,23 \} .$
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