Question

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

Answer 1

`x`=`3//2`

Explanation:

We have, `2x+frac{3}4=3x-frac{3}4`
On further simplification, `2xx frac{3}4=3x-2x`
Or, `frac{3}2=x`

Answer 2

`x=3/2" "` Using First principles

A lot of detail given so that you can see where everything comes from. You would normally do this in just a few lines.

Explanation:

Given `2x+3/4=3x-3/4`

The `3x` on the right of = is greater than the `2x` on the left. So to keep the `x` terms positive we move the `2x` on the left to the right. We do this by changing the `2x` into 0.

Subtract `color(red)(2x)` from both sides

#color(green)(2x+3/4=3x-3/4color(white)("dddd")->color(white)("dddd)ubrace(2x color(red)(-2x))+3/4=ubrace(3x color(red)(-2x))-3/4 )#
`color(green)(color(white)("ddddddddddddddddddddddddddd")darrcolor(white)("dddddddddd")darr)`
`color(green)(color(white)("ddddddddddddddddddd")->color(white)("d.dddd")0color(white)("d.d")+3/4 =color(white)("dd")xcolor(white)("d.d")-3/4)`

Now we need to get the `x` on its own so we need to turn the `-3/4` onto 0.

Add `color(red)(3/4)` to both sides

`color(green)(3/4=x-3/4color(white)("ddddddddd")->color(white)("dddd")ubrace(3/4color(red)(+3/4))=xcolor(white)("d")ubrace(-3/4color(red)(+3/4)))`

`color(green)(color(white)("dddddddddddddddddd")->color(white)("dddddd") 3/2color(white)("dd")=xcolor(white)("d")+0)`

`color(green)(color(white)("dddddddddddddddddd")->color(white)("ddddddd.d")x=3/2)`