#### Answer

a) Yes
b) No

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Substitute the given value for $x$ in the given equation, $
\sqrt{3x+18}-x=0
.$ 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 $
6
,$ in the given equation results to
\begin{array}{l}\require{cancel}
\sqrt{3(6)+18}-6=0
\\\\
\sqrt{18+18}-6=0
\\\\
\sqrt{36}-6=0
\\\\
6-6=0
\\\\
0=0
\text{ (TRUE)}
.\end{array}
Hence, $x=
6
$ is a solution to the given equation.
b) Substituting $x$ with $
-3
,$ in the given equation results to
\begin{array}{l}\require{cancel}
\sqrt{3(-3)+18}-(-3)=0
\\\\
\sqrt{-9+18}+3=0
\\\\
\sqrt{9}+3=0
\\\\
3+3=0
\\\\
6=0
\text{ (FALSE)}
.\end{array}
Hence, $x=
-3
$ is NOT a solution to the given equation.