## College Algebra (11th Edition)

$x=-2$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\sqrt[5]{2x}=\sqrt[5]{3x+2} ,$ raise both sides to the fifth power. Then isolate the variable. $\bf{\text{Solution Details:}}$ Raising both sides to the fifth power, the given equation is equivalent to \begin{array}{l}\require{cancel} 2x=3x+2 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 2x-3x=2 \\\\ -x=2 \\\\ x=-2 .\end{array}