Answer
$x= 1 $
Work Step by Step
Given \begin{equation}
\sqrt{7 x+2}=3.
\end{equation} First square both sides to eliminate the radical sign and solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt{7 x+2}&=3\\
\left(\sqrt{7 x+2}\right)^2&= 3^2\\
7 x+2& = 9 \\
x&= \frac{9-2}{7}\\
& = 1.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt{7 \cdot 1+2}&\stackrel{?}{=}3\\
3& =3\quad \checkmark.
\end{aligned}
\end{equation} The solution is $x= 1 $.
