Question

How do you solve `3x + \frac { 5} { 2} = 5x + \frac { 4} { 3}`?

Answer 1

Collect like terms and then solve for `x`.

`x=7/12`

Explanation:

This one turns out to be fairly easy:

`3x + 5/2 = 5x + 4/3`

Subtract `3x` from both sides:

`5/2 = 2x + 4/3`

Subtract `4/3` from both sides (and swap the sides)

`2x = 5/2 - 4/3`

We need a common denominator, so multiply `3/3xx5/2=15/6` and `2/2xx-4/3=-8/6`

`2x = 15/6-8/6=7/6`

Now divide both sides by 2:

`x=7/12`

Answer 2

The answer is `7/12`.

Explanation:

First of all, you move the constant `+5/2` to the right, the same for `5x` but to the left (and don't forget for both to change its sign) which gives us

`3x-5x=4/3-5/2`

`=> -2x = 8/6-15/6`

`=> -2x = -7/6`

Then to find `x` you divide both sides by `-2`, which gives us `7/12`.