Answer
$x=-1$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt{8-x}+7=10
$, is equivalent to
\begin{array}{l}
\sqrt{8-x}=10-7
\\\\
\sqrt{8-x}=3
.\end{array}
Raising both sides to the $\text{
2nd
}$ power, the solution to the equation above, $
\sqrt{8-x}=3
$, is
\begin{array}{l}
8-x=9
\\\\
-x=9-8
\\\\
-x=1
\\\\
x=-1
.\end{array}
Upon checking, $
x=-1
$ satisfies the given equation.