Question

Solve:
$\frac{2-7x}{1-5x}=\frac{3+7x}{4+5x}$

Answer 1

$$\begin{gathered} \frac{2-7x}{1-5x}=\frac{3+7x}{4+5x} \\ \Rightarrow (4+5x)(2-7x)=(1-5x)(3+7x)(\mathrm{by}\mathrm{cross}\mathrm{multiplication}) \\ \Rightarrow 8-28x+10x-35x^2=3+7x-15x-35x^2 \\ \Rightarrow -35x^2-18x+8=-35x^2-8x+3 \\ \Rightarrow -35x^2+35x^2-18x+8x=-8+3 \\ \Rightarrow -10x=-5 \\ \Rightarrow x=\frac{-5}{-10}=\frac{1}{2} \\ \therefore x=\frac{1}{2} \end{gathered}$$