Answer
$45$
Work Step by Step
$\frac{1}{2}\left( x-7 \right)=\frac{1}{3}x+4$
Multiply both sides by the least common denominators, $2$ and $3$.
$\begin{align}
& \frac{1}{2}\left( x-7 \right)=\frac{1}{3}x+4 \\
& 6\times \frac{1}{2}\left( x-7 \right)=6\times \left( \frac{1}{3}x+4 \right) \\
& 3\left( x-7 \right)=2x+24 \\
& 3x-21=2x+24
\end{align}$
Subtract $\left( 2x \right)$ from both sides.
$\begin{align}
& 3x-21-2x=2x+24-2x \\
& x-21=24
\end{align}$
Add $\left( 21 \right)$ on both sides,
$\begin{align}
& x-21=24 \\
& x-21+21=24+21 \\
& x=45
\end{align}$
Thus, the required value is $x=45$.
