# How do I solve an equation with a variable in the numerator?

## Homework Statement

I just missed a 16-point question on a quiz because I didn't know how to separate the variable. It was an absolute value equation, but I just need to know how to deal with a variable in a fraction. Here's what it looked like:

(5x+10)/2 = 20

## The Attempt at a Solution

I tried multiplying everything by the denominator, but I'm not sure if or why that works. Any help would be greatly appreciated, thanks!

Borek
Mentor
Multiplying by denominator should work. You can do anything that doesn't change the equality - that means adding, subtracting, multiplying or dividing both sides of the equation by the same thing.

Or you could write the fraction as $\frac {5x}{2} + \frac {10}{2}$.

Thanks!

The easiest way is to multiply both sides of the equation by the denominator. The reason why this works is because it doesn't change the equality.

(5x+10)/2 = 20
5x+10 = 40
5x = 30
x = 6

Even if the variable was in the denominator, you can still solve for the variable using the same steps.

2/(5x+10) = 20
2 = 100x + 200
-198 = 100x
-198/100 = x
x = -99/50