Chapter 2 - Equations, Inequalities, and Problem Solving - Review Exercises: Chapter 2: 63

$n=\{ -20,20 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $|3n|=60 ,$ use the definition of absolute value equality. Then use the properties of equality to solve 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} 3n=60 \\\\\text{OR}\\\\ 3n=-60 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 3n=60 \\\\ n=\dfrac{60}{3} \\\\ n=20 \\\\\text{OR}\\\\ 3n=-60 \\\\ n=-\dfrac{60}{3} \\\\ n=-20 .\end{array} Hence, $n=\{ -20,20 \} .$

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