## Intermediate Algebra (12th Edition)

$x=7$
$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $\sqrt{4x-2}=\sqrt{3x+5} ,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation. $\bf{\text{Solution Details:}}$ Squaring both sides of the equation results to \begin{array}{l}\require{cancel} \left( \sqrt{4x-2} \right)^2=\left( \sqrt{3x+5} \right)^2 \\\\ 4x-2=3x+5 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 4x-3x=5+2 \\\\ x=7 .\end{array} Upon checking, $x=7$ satisfies the original equation.