# How do you solve \frac { 6} { 7x } = \frac { 4} { 5x - 1}?

Dec 9, 2016

Multiply the fractions on each side of the equation by the same factor, which is the product of the denominators ($7 x \left(5 x - 1\right)$), to clear the fractions and keep the equation balanced:

$\frac{7 x \left(5 x - 1\right) \cdot 6}{7 x} = \frac{7 x \left(5 x - 1\right) \cdot 4}{5 x - 1}$

$\frac{\cancel{7 x} \left(5 x - 1\right) \cdot 6}{\cancel{7 x}} = \frac{7 x \cancel{\left(5 x - 1\right)} \cdot 4}{\cancel{\left(5 x - 1\right)}}$

$\left(5 x - 1\right) \cdot 6 = 7 x \cdot 4$

We can now solve for $x$ using the necessary mathematics while keeping the equation balanced:

$30 x - 6 = 28 x$

$30 x - 28 x - 6 + 6 = 28 x - 28 x + 6$

$2 x = 6$

$\frac{2 x}{2} = \frac{6}{2}$

$x = 3$