how do you solve an algebra equation with fractions with different denominators?

Question

ive got this algebra question that im stuck on:

 

6x - (2x+3)/5 = (x-5)/4  - x

 

how do you solve by changing the denominators?

Answer 1

You need common denominators. To subtract (2x+3)/5 from 6x, you need both to be over the same denominator. Look at 6x as "6x / 1". To get the least common denominator, find the least common multiple (LCM) of your denominators (for 1 and 5, this is 5).

 

To put (2x+3)/5 over 5, you don't need to do anything, since it's already over 5. To put 6x / 1 over 5, you need to multiply both its numerator (top) and denominator (bottom) by 5. Also known as multiplying 6x / 1 by 5 / 5 = 30x / 5.

 

Now, you can combine the fractions, to get [30x - (2x + 3)] / 5. Combine like terms to get (28x - 3)/5, for that side of your equation.

 

Do the same thing for the other side of the equation, and then solve it like a normal algebraic equation.