#### Answer

a) Yes
b) Yes

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Substitute the given value for $x$ in the given equation, $
\sqrt{3x-3}-x+1=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 $
1
,$ in the given equation results to
\begin{array}{l}\require{cancel}
\sqrt{3(1)-3}-1+1=0
\\\\
\sqrt{3-3}+0=0
\\\\
\sqrt{0}=0
\\\\
0=0
\text{ (TRUE)}
.\end{array}
Hence, $x=
0
$ is a solution to the given equation.
b) Substituting $x$ with $
4
,$ in the given equation results to
\begin{array}{l}\require{cancel}
\sqrt{3(4)-3}-4+1=0
\\\\
\sqrt{12-3}-3=0
\\\\
\sqrt{9}-3=0
\\\\
3-3=0
\\\\
0=0
\text{ (TRUE)}
.\end{array}
Hence, $x=
4
$ is a solution to the given equation.