Question

Solve the following:

$\frac{(y–(4–3y\left)\right)}{(2y–(3+4y\left)\right)}=\frac{1}{5}$

Answer 1

$\frac{(y–(4–3y\left)\right)}{(2y–(3+4y\left)\right)}=\frac{1}{5}$

We have to find the value of $y$

$$\begin{gathered} \frac{(y–(4–3y\left)\right)}{(2y–(3+4y\left)\right)}=\frac{1}{5} \\ \Rightarrow \frac{y-4+3y}{2y-3-4y}=\frac{1}{5} \\ \Rightarrow \frac{4y-4}{-2y-3}=\frac{1}{5} \\ \Rightarrow 5(4y-4)=1(-2y-3) \\ \Rightarrow 20y-20=-2y-3 \\ \Rightarrow 20y+2y=-3+20 \\ \Rightarrow 22y=17 \\ \Rightarrow y=\frac{17}{22} \end{gathered}$$

Hence, $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{17}}{\mathbf{22}}$ is the solution of given equation.