Answer
$x=\frac{76}{3} $
Work Step by Step
Given \begin{equation}
\sqrt[4]{3 x+5}-7=-4.
\end{equation} First rearrange the equation and square both sides to eliminate the radical signs (may be repeated), and solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[4]{3 x+5}-7&=-4\\
\sqrt[4]{3 x+5}&=3\\
\left(\sqrt[4]{3 x+5}\right)^4&= 3^4\\3 x+5& = 81 \\
x&= \frac{81-5}{3}\\& = \frac{76}{3}.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt[4]{3\cdot \frac{76}{3} +5}-7&\stackrel{?}{=}-4\\
-4& =-4\quad \quad \textbf{True}.
\end{aligned}
\end{equation} The solution is $x=\frac{76}{3} $.
