Answer
$z=6$.
Work Step by Step
The given equation is
$\Rightarrow \frac{1}{2}z+4=\frac{5}{2}z-8$
Add $8-\frac{1}{2}z$ to each side.
$\Rightarrow \frac{1}{2}z+4+8-\frac{1}{2}z=\frac{5}{2}z-8+8-\frac{1}{2}z$
Simplify.
$\Rightarrow 12=\frac{5-1}{2}z$
$\Rightarrow 12=\frac{4}{2}z$
$\Rightarrow 12=2z$
Divide each side by $2$.
$\Rightarrow \frac{12}{2}=\frac{2z}{2}$
Simplify.
$\Rightarrow 6=z$.
Check:- $z=6$
$\Rightarrow \frac{1}{2}(6)+4=\frac{5}{2}(6)-8$
$\Rightarrow 3+4=15-8$
$\Rightarrow 7=7$
True.
Hence, the solution is $z=6$.
