## Algebra: A Combined Approach (4th Edition)

$x=\dfrac{1}{2}$
$\bf{\text{Solution Outline:}}$ 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.