Answer
$x= 4.5$
Work Step by Step
Given
\begin{equation}
\sqrt{x+2}=\sqrt{3 x-7}.
\end{equation} Start by squaring both sides to eliminate the radical sign on both sides and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt{x+2}&=\sqrt{3 x-7}\\
\left(\sqrt{x+2}\right)^{2} & =\left(\sqrt{3 x-7}\right)^{2} \\
x+2& =3x-7\\
9 & = 2x \\
4.5& =x.
\end{aligned}
\end{equation} Check: \begin{equation}
\begin{aligned}
\sqrt{4.5+2}& \stackrel{?}{=} \sqrt{3 (4.5)-7} \\
\sqrt{6.5} & = \sqrt{6.5} \quad \text { True } \\
\end{aligned}
\end{equation} The solution is $x= 4.5$.
