# How do you solve for x in y = (1+4x)/(7-9x)?

Aug 18, 2016

$x = \frac{7 y - 1}{9 y + 4} , \mathmr{if} , y \ne - \frac{4}{9}$.

#### Explanation:

Given that, $y = \frac{1 + 4 x}{7 - 9 x}$

$\Rightarrow y \left(7 - 9 x\right) = 1 + 4 x , i . e . , 7 y - 9 x y = 1 + 4 x$.

$\Rightarrow 7 y - 1 = 9 x y + 4 x = x \left(9 y + 4\right)$.

$\Rightarrow \frac{7 y - 1}{9 y + 4} = x , \mathmr{if} , y \ne - \frac{4}{9}$.