Answer
$x=\dfrac{80}{3}$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[4]{3x+1}-4=-1
$, is equivalent to
\begin{array}{l}
\sqrt[4]{3x+1}=-1+4
\\\\
\sqrt[4]{3x+1}=3
.\end{array}
Raising both sides to the $\text{
4th
}$ power, the solution to the equation above, $
\sqrt[4]{3x+1}=3
$, is
\begin{array}{l}
3x+1=81
\\\\
3x=81-1
\\\\
3x=80
\\\\
x=\dfrac{80}{3}
.\end{array}
Upon checking, $
x=\dfrac{80}{3}
$ satisfies the given equation.