Answer
$w=30$
Work Step by Step
The given equation is
$\Rightarrow 15=6+\sqrt{3w-9}$
Subtract $6$ from each side.
$\Rightarrow 15-6=6+\sqrt{3w-9}-6$
Simplify.
$\Rightarrow 9=\sqrt{3w-9}$
Square each side of the equation.
$\Rightarrow 9^2=(\sqrt{3w-9})^2$
Simplify.
$\Rightarrow 81=3w-9$
Add $9$ to each side.
$\Rightarrow 81+9=3w-9+9$
Simplify.
$\Rightarrow 90=3w$
Divide each side by $3$.
$\Rightarrow \frac{90}{3}=\frac{3w}{3}$
Simplify.
$\Rightarrow 30=w$
Check $w=30$.
$\Rightarrow 15=6+\sqrt{3w-9}$
$\Rightarrow 15=6+\sqrt{3(30)-9}$
$\Rightarrow 15=6+\sqrt{90-9}$
$\Rightarrow 15=6+\sqrt{81}$
$\Rightarrow 15=6+9$
$\Rightarrow 15=15$
True.
Hence, the solution is $w=30$.
