Answer
$x=4$
Work Step by Step
Squaring both sides of the inequality and using the properties of radicals, the solution to the given equation is
\begin{array}{l}\require{cancel}\left(
\sqrt{6x+1}
\right)^2=\left(
\sqrt{3x+13}
\right)^2
\\\\
6x+1=3x+13
\\\\
6x-3x=13-1
\\\\
3x=12
\\\\
x=\dfrac{12}{3}
\\\\
x=4
.\end{array}
Upon checking, $
x=4
$ satisfies the original equation.
