Question

Solve for $x$:

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

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

Answer: (B)

$\frac{1}{2}$

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

Applying Alternendo,

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

Now applying Componendo and Dividendo,

$\Rightarrow \frac{(2-7x)+(3+7x)}{(2-7x)-(3+7x)}=\frac{(1-5x)+(4+5x)}{(1-5x)-(4+5x)}$

$\Rightarrow \frac{5}{-1-14x}=\frac{5}{-3-10x}$

$\Rightarrow -1-14x=-3-10x$

$\Rightarrow 14x-10x=3-1$

$\Rightarrow 4x=2$

$\Rightarrow x=\frac{2}{4}=\frac{1}{2}$