Question

Solve:
$\frac{2-9z}{17-4z}=\frac{4}{5}$

Answer 1

$$\begin{gathered} \frac{2-9z}{17-4z}=\frac{4}{5} \\ \Rightarrow 5(2-9z)=4(17-4z)(\mathrm{by}\mathrm{cross}\mathrm{multiplication}) \\ \Rightarrow 10-45z=68-16z \\ \Rightarrow 10-68=45z-16z \\ \Rightarrow -58=29z \\ \Rightarrow 29z=-58(\mathrm{by}\mathrm{transposition}) \\ \Rightarrow z=\frac{-58}{29}=-2 \\ \therefore z=-2 \end{gathered}$$