Answer
$x=\dfrac{9}{2}$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt{2x}-1=2
$, is equivalent to
\begin{array}{l}
\sqrt{2x}=2+1
\\\\
\sqrt{2x}=3
.\end{array}
Raising both sides to the $\text{
2nd
}$ power, the solution to the equation above, $
\sqrt{2x}=3
$, is
\begin{array}{l}
2x=9
\\\\
x=\dfrac{9}{2}
.\end{array}
Upon checking, $
x=\dfrac{9}{2}
$ satisfies the given equation.