#### Answer

$x=\dfrac{1}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\sqrt{2x-1}=\sqrt{1-2x}
,$ raise both sides to the exponent equal to the index of the radical. Then use the properties of equality to isolate the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Get rid of the radical symbol by raising both sides of the equation above to the exponent equal to $
2
$ (the same index as the radical). This results to
\begin{array}{l}\require{cancel}
(\sqrt{2x-1})^2=(\sqrt{1-2x})^2
\\\\
2x-1=1-2x
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
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.