## Intermediate Algebra (12th Edition)

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