## Intermediate Algebra (12th Edition)

$\bf{\text{Solution Outline:}}$ 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.