Question

How do you solve `5/7x-3/14=-3/8x+3/4`?

Answer 1

`x=54/61`

Explanation:

The easiest way to solve this is to get rid of the denominators first.
The least common multiple of 7, 14, 8 and 4 would be `7*8=4*14=56`.

Therefore, multiply both sides with 56=4*14:
`(5/7x-3/14)*4*14=(-3/8x+3/4)*8*7`

Simplifying we get:
`5*8x-3*4=-3*7x+3*14`
or: `40x-12=-21x+42`

Adding `21x+12` to both sides to get the x terms to the left and the constants to the right, we get:
`40x+21x= 42+12`
`61x=54`
Dividing on 61 on both sides we get
`x=54/61`

As `61` is a prime number, we cannot simplify this more .