Question

If $\frac{2}{3x+1}=\frac{5}{x+\frac{1}{4}}$, then $x$ is equal to

• A. $x=-\frac{9}{26}$
• B. $x=\frac{5}{13}$
• C. $x=\frac{13}{6}$
• D. $x=-\frac{26}{9}$

Answer 1

The correct option is A $x=-\frac{9}{26}$

Given, $\frac{2}{3x+1}=\frac{5}{x+\frac{1}{4}}$

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

$\Rightarrow \frac{2}{3x+1}=\frac{20}{4x+1}$

On cross multiplying, weget

$2(4x+1)=20(3x+1)$

$\Rightarrow 4x+1=10(3x+1)$

$\Rightarrow 4x+1=30x+10$

Putting $x$ terms on one side and constants to another side.

$\Rightarrow 4x-30x=10-1$

$\Rightarrow -26x=9$

$\Rightarrow x=-\frac{9}{26}$