Solve $\frac{2-7\mathrm{x}}{1-5\mathrm{x}}=\frac{3+7\mathrm{x}}{4+5\mathrm{x}}$and choose the option which represents the solution correctly.

 

The given linear equation is as follows,
$\frac{2-7x}{1-5x}=\frac{3+7x}{4+5x}$.
We cross-multiply the denominators with the numerators on the either side as follows,
 

$\begin{array}{c}8-18x-35x^2+35x^2=3-8x-35x^2+35x^2\\ 8-18x=3-8x\end{array}$
$\begin{array}{c}8-18x+8x=3-8x+8x\\ 8-10x=3\\ 8-8-10x=3-8\\ -10x=-5\end{array}$
$\begin{array}{c}\frac{-10\mathrm{x}}{-10}=\frac{-5}{-10}\\ \mathrm{x}=\frac{1}{2}\end{array}$
So, the value of the variable x is $\frac{1}{2}$.