#### Answer

$x=11$

#### Work Step by Step

Using the properties of equality, the given equation, $
\sqrt{x-2}-7=-4
$, is equivalent to
\begin{array}{l}
\sqrt{x-2}=-4+7
\\\\
\sqrt{x-2}=3
.\end{array}
Raising both sides to the $\text{
2nd
}$ power, the solution to the equation above, $
\sqrt{x-2}=3
$, is
\begin{array}{l}
x-2=9
\\\\
x=9+2
\\\\
x=11
.\end{array}
Upon checking, $
x=11
$ satisfies the given equation.