Answer
$x=5$
Work Step by Step
Using the properties of equality, the given equation, $
(3x+7)^{1/3}-(4x+2)^{1/3}=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3x+7)^{1/3}=(4x+2)^{1/3}
.\end{array}
Raising both sides of the equation to the $\text{
third
}$ power, the solution/s is/are
\begin{array}{l}\require{cancel}
3x+7=4x+2
\\\\
3x-4x=2-7
\\\\
-x=-5
\\\\
x=5
.\end{array}