Question

How do you solve `3/4 = 3/8x - 3/2`?

Answer 1

My first step would be to multiply everything on both sides by `8` to get rid of all the fractions.

Explanation:

`->6=3x-12->18=3x->x=6`

Answer 2

I found: `x=6`

Explanation:

I would take `8` as common denominator and write:
`(color(red)(2)*3)/8=(3x)/8-(color(red)(4)*3)/8`
where the red terms were introduced to adapt the numerators to the new denominator `8`.
I can now get rid of the denominators and get:
`(2*3)/cancel(8)=(3x)/cancel(8)-(4*3)/cancel(8)`
`6=3x-12`
and:
`3x=18`
`x=18/3=6`

Answer 3

`x=6`

Explanation:

OK, we are given `3/4=3/8x-3/2`

First, let's add `3/2` to both sides:

`3/4=3/8x-3/2`

`3/4+3/2=3/8x`

We need a common denominator for both `3/4` and `3/2`, so we'll go with the common denominator of `4`, since both `2` and `4` go into `4`:

`3/4+3/2=3/8x`

`3/4+(2*3)/(2*2)=3/8x`

`3/4+6/4=3/8x`

Now, add `3/4+6/4` to get `9/4`

`3/4+6/4=3/8x`

`9/4=3/8x`

Now, multiply both sides by the reciprocal of `3/8` which is `8/3`

`9/4=3/8x`

`8/3*9/4=8/3*3/8x`

`2/1*3/1=1*x`

`2*3=x`

`6=x`