Answer
$x=5$
Work Step by Step
Squaring both sides of the equation and using the properties of radicals, the solution to the given equation is
\begin{array}{l}\require{cancel}\left(
\sqrt{3x+1}
\right)^2=\left(
4
\right)^2
\\\\
3x+1=16
\\\\
3x=16-1
\\\\
3x=15
\\\\
x=\dfrac{15}{3}
\\\\
x=5
.\end{array}
Upon checking, $
x=5
$ satisfies the original equation.
