Answer
$x=0$
Work Step by Step
Raising both sides of the equation to the $\text{
fourth
}$ power, the solution/s to the given equation, $
\sqrt[4]{3x+1}=1
,$ is/are
\begin{array}{l}\require{cancel}
3x+1=1
\\\\
3x=1-1
\\\\
3x=0
\\\\
x=\dfrac{0}{3}
\\\\
x=0
.\end{array}
Upon checking, $
x=0
$ satisfies the original equation.