# How do you solve 7/x=8/(5x-6)?

Jul 9, 2016

The answer to that problem is $\frac{14}{9}$

#### Explanation:

In the equation, you need to remove the denominator in both sides of the given equation. To do that, you need to multiply both sides by their corresponding denominator.

$\left(5 x - 6\right) \left(x\right) \left(\frac{7}{x}\right) = \left(5 x - 6\right) \left(x\right) \left(\frac{8}{5 x - 6}\right)$

Simplify

$\left[\frac{\left(5 x - 6\right) \left(x\right) \left(7\right)}{x}\right] = \left[\frac{\left(5 x - 6\right) \left(x\right) \left(8\right)}{5 x - 6}\right]$

$7 \left(5 x - 6\right) = 8 x$

$35 x - 42 = 8 x$

$35 x - 42 + 42 = 8 x + 42$

$35 x - 8 x = 8 x - 8 x + 42$

$27 x = 42$

$\frac{27 x}{27} = \frac{42}{27}$

$x = \frac{42}{27}$

Simplify the answer to the lowest term

$x = \frac{42}{27} \div \frac{3}{3}$

Since both of them has the factor of 3, we will divide both the numerator and the denominator by 3.

$x = \frac{14}{9}$