Answer
$x= 24.6 $
Work Step by Step
Given \begin{equation}
\sqrt[3]{5 x+2}+7=12.
\end{equation} Start by rewriting the radical as a power of fraction and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[3]{5 x+2}+7&=12\\
\left(5 x+2\right)^{\frac{1}{3}}&= 5\\
\left(\left(5 x+2\right)^{\frac{1}{3}}\right)^3& = \left( 5\right)^3 \\
5 x+2& =125\\
x&= \frac{125-2}{5}\\
& = 24.6.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt[3]{5 (24.6)+2}+7&\stackrel{?}{=}12\\
12& =12\quad \checkmark.
\end{aligned}
\end{equation} The solution is $x= 24.6 $.
