## Algebra: A Combined Approach (4th Edition)

$x=45$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\sqrt{3x+9}=12 ,$ raise both sides to the exponent equal to the index of the radical. Then use the properties of equality to isolate the variable. Finally, do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Get rid of the radical symbol by raising both sides of the equation above to the exponent equal to $2$ (the same index as the radical). This results to \begin{array}{l}\require{cancel} (\sqrt{3x+9})^2=12^2 \\\\ 3x+9=144 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 3x=144-9 \\\\ 3x=135 \\\\ x=\dfrac{135}{3} \\\\ x=45 .\end{array} Upon checking, $x=45$ satisfies the original equation.