Question

How do you solve `1/3m=1/4m-2`?

Answer 1

Multiply both sides by `12`, subtract `3m` from both sides to get `m=-24`

Explanation:

The original equation is
`1/3 m = 1/4 m -2`

Fractions are difficult to deal with, so we're going to get rid of them by multiplying the whole equation by the Least Common Multiple of the two denominators, `3` and `4`, which is `12`.
`1/3 m = 1/4 m -2`
`12/3 m = 12/4 m -24`
`4m = 3m -24`

Now we need to move all of the terms with variables to one side, so we subtract `3m` from both sides.

`4m = 3m - 24`
`4m - 3m = 3m - 3m - 24`
`m = -24`
which is our answer. `square`

Answer 2

`m = -24`

Explanation:

When you have an equation with fractions, you can get rid of them by multiplying by the LCD, which in this case is 12, which allows you to cancel the denominators.

`(color(red)cancel12^4 xx1)/cancel3m =(color(red)cancel12^3 xx1)/cancel4m -color(red)12xx2`

`4m = 3m-24" "larr` much better, no fractions!

`4m-3m=-24`

`m = -24`