#### Answer

a) Yes
b) No

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Substitute the given value for $x$ in the given equation, $
\sqrt{x+2}-\sqrt{9x-2}=-2\sqrt{x-1}
.$ If the left side of the equation becomes equal to the right side of the equation, then the given value of $x$ is a solution to the equation.
$\bf{\text{Solution Details:}}$
a) Substituting $x$ with $
2
,$ in the given equation results to
\begin{array}{l}\require{cancel}
\sqrt{2+2}-\sqrt{9(2)-2}=-2\sqrt{2-1}
\\\\
\sqrt{4}-\sqrt{18-2}=-2\sqrt{1}
\\\\
2-\sqrt{16}=-2(1)
\\\\
2-4=-2
\\\\
-2=-2
\text{ (TRUE)}
.\end{array}
Hence, $x=
2
$ is a solution to the given equation.
b) Substituting $x$ with $
7
,$ in the given equation results to
\begin{array}{l}\require{cancel}
\sqrt{7+2}-\sqrt{9(7)-2}=-2\sqrt{7-1}
\\\\
\sqrt{9}-\sqrt{63-2}=-2\sqrt{6}
\\\\
3-\sqrt{61}=-2\sqrt{6}
\text{ (FALSE)}
.\end{array}
Hence, $x=
7
$ is NOT a solution to the given equation.