## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$w=\{ -15,15 \}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $3|w|-8=37 ,$ 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 given expression is equivalent to \begin{array}{l}\require{cancel} 3|w|-8=37 \\\\ 3|w|=37+8 \\\\ 3|w|=45 \\\\ |w|=\dfrac{45}{3} \\\\ |w|=15 .\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} w=15 \\\\\text{OR}\\\\ w=-15 .\end{array} Hence, $w=\{ -15,15 \} .$