Answer
$x=\left\{ -10, -\dfrac{4}{3}\right\}$
Work Step by Step
Using the properties of absolute value, the given equation, $
|x-3|=|7+2x|
,$ is equivalent to
\begin{array}{l}\require{cancel}
x-3=7+2x
\\\text{ or }\\
x-3=-(7+2x)
.\end{array}
Using $V=\pi r^2h,$ with $r=3$ and $h=6,$ then the volume of the cylinder is
\begin{array}{l}\require{cancel}
x-3=7+2x
\\
x-2x=7+3
\\
-x=10
\\
x=-10
\\\\\text{ or }\\\\
x-3=-(7+2x)
\\
x-3=-7-2x
\\
x+2x=-7+3
\\
3x=-4
\\
x=-\dfrac{4}{3}
.\end{array}
Hence, the solution set is $
x=\left\{ -10, -\dfrac{4}{3}\right\}
.$
