# How do you solve 4/(9y-6)=2?

Feb 6, 2016

Step by step explanation is given blow

#### Explanation:

$\frac{4}{9 y - 6} = 2$

Think of this as a proportion

$\frac{4}{9 y - 6} = \frac{2}{1}$

We know if $\frac{a}{b} = \frac{c}{d}$ Then $\frac{b}{a} = \frac{d}{c}$

Basically we are flipping and that would help us

$\frac{9 y - 6}{4} = \frac{1}{2}$

Let us multiply $4$ on both the sides

$\cancel{4} \times \frac{9 y - 6}{\cancel{4}} = 4 \times \frac{1}{2}$

$9 y - 6 = 2$

To solve for $y$ we need to undo all that has been done to it, for this we shall use the inverse operations.

Let us start with $- 6$ we add $6$ on both the sides and we get

$9 y - \cancel{6} + \cancel{6} = 2 + 6$
$9 y = 8$

$y$ is multiplied by $9$ to undo it we divide both sides by $9$

$\frac{\cancel{9} y}{\cancel{9}} = \frac{8}{9}$

$y = \frac{8}{9}$

Let us check if our solution is correct by plugging $y = \frac{8}{9}$ in the original problem.

$\frac{4}{9 y - 6} = 2$
$\frac{4}{9 \left(\frac{8}{9}\right) - 6} = 2$
$\frac{4}{8 - 6} = 2$
$\frac{4}{2} = 2$
$2 = 2 \quad$ this is a true statement so the solution is valid.

$y = \frac{8}{9}$