Question

Solve:
$4-\frac{2(z-4}{3}=\frac{1}{2}(2z+5)$

Answer 1

$$\begin{gathered} 4-\frac{2(z-4)}{3}=\frac{1}{2}(2z+5) \\ \Rightarrow \frac{12-2(z-4)}{3}=\frac{1(2z+5)}{2}(\mathrm{L}.\mathrm{C}.\mathrm{M}.\hspace{0.17em}\mathrm{of}1\mathrm{and}3\mathrm{is}3) \\ \Rightarrow \frac{12-2z+8}{3}=\frac{2z+5}{2} \\ \Rightarrow \frac{20-2z}{3}=\frac{2z+5}{2} \\ \Rightarrow 2(20-2z)=3(2z+5)(\mathrm{by}\mathrm{cross}\mathrm{multiplication}) \\ \Rightarrow 40-4z=6z+15 \\ \Rightarrow 40-15=6z+4z \\ \Rightarrow 25=10z \\ \Rightarrow 10z=25(\mathrm{by}\mathrm{transposition}) \\ \Rightarrow z=\frac{25}{10}=\frac{5}{2} \\ \therefore z=\frac{5}{2} \end{gathered}$$