Answer
$x=\dfrac{1}{2}$
Work Step by Step
Raising both sides of the given equation, $
\sqrt[]{2x-1}=\sqrt[]{1-2x}
,$ to the second power, then the solution/s is/are
\begin{array}{l}\require{cancel}
2x-1=1-2x
\\\\
2x+2x=1+1
\\\\
4x=2
\\\\
x=\dfrac{2}{4}
\\\\
x=\dfrac{1}{2}
.\end{array}
Upon checking, $
x=\dfrac{1}{2}
$ satisfies the original equation.