#### Answer

$x=-2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}