Answer
The solution set is $\left\{ 45 \right\}$.
Work Step by Step
Consider the equation $24+3\left( x+2 \right)=5\left( x-12 \right)$.
Apply the distributive property
$\begin{align}
& 24+3\left( x+2 \right)=5\left( x-12 \right) \\
& 24+3\left( x \right)+3\left( 2 \right)=5\left( x \right)+5\left( -12 \right) \\
& 24+3x+6=5x-60
\end{align}$
Collect all variables on one side.
$\begin{align}
& 24+3x+6=5x-60 \\
& 30+60=5x-3x \\
& 90=2x
\end{align}$
Divide both sides of the equation by $2$.
$\begin{align}
& \frac{90}{2}=\frac{2x}{2} \\
& 45=x
\end{align}$
The solution of the equation $24+3\left( x+2 \right)=5\left( x-12 \right)$ is $45$.
Check the obtained solution by substituting $x=45$ in the equation $24+3\left( x+2 \right)=5\left( x-12 \right)$
$\begin{align}
& \text{ }24+3\left( x+2 \right)=5\left( x-12 \right) \\
& 24+3\left( 45+2 \right)\overset{?}{\mathop{=}}\,5\left( 45-12 \right) \\
& \text{ }24+141\overset{?}{\mathop{=}}\,165 \\
& \text{ }165\overset{?}{\mathop{=}}\,165 \\
\end{align}$
This is true.
Hence, the value satisfies the above equation.
