Question

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

Answer 1

With practice you can do these quicker as you learn the shortcut.

`x=7`

Explanation:

Objective is to have a single `x` on one side of the = and everything else on the other side.

Given:`" "color(green)(2x+3=3x-4)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Step 1 ")color(brown)("Having all the "x" terms on one side of =")`

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

`color(green)(2xcolor(red)(-2x)+3=3xcolor(red)(-2x)-4)`

`0+3=x-4`

Swap round

`x-4=3`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2 ")color(brown)("Have just "x" on the left of =")`

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

`color(green)(x-4color(red)(+4)=3color(red)(+4))`

`x=7`