Question

What is the value of x when `2x+3=3x-4`?

Answer 1

x = 7

Explanation:

x is an unknown think of it as something that has been lost.
When something has been lost it is important to work backwards.

The order of operation is PE MDAS. working backwards gives
The order for solving as PE SAD M Think of it this was

If you lose something in PE you are a SAD Man ( or Mam depending on gender.

So do P parenthesis and Exponents first (PE) The do Subtract and Addition at the same time (SA). The do Division and Multiplication at same time ( DM)

In this problem start by adding + 4 ( -4 backwards) to both sides of the equation.

`2x + 3 + 4 = 3x -4 + 4` ; `-4 + 4 =0` so

`2x + 7 = 3x` Subtract -2x from both sides ( +2x backwards)

`2x -2x + 7 = 3x -2x` :( 3x -2x = 1 x) so

+7 = 1 x dividing both sides by 1 doesn't change the answer

x = +7

Answer 2

`x=7`

Explanation:

The objective is to have a single `x` on one side of the = sign and everything else on the other sides

Given:`" "2x+3=3x-4`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Step 1 - move all the terms of "x" to 1 side only")`

`+3x` is greater than `+2x` so move the `2x` to keep `x` positive.

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

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

But `2x-2x=0` and `3x-2x=x` giving:

`0+3" "=" "x-4`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2- move the -4 so that we have "x" on its own")`

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

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

But -4 + 4 = 0

`7=x+0`

`" "color(maroon)(ul(bar(|color(white)(2/2)x=7color(white)(..)|)))`

Answer 3

`x=7`

Explanation:

`2x+3=3x-4`

`:.2x-3x=-4-3`

`:.-x=-7`

multiply both sides by`-1`

`:.x=7`

substitute `x=7`

`:.2(7)+3=3(7)-4`

`:.14+3=21-4`

`:.17=17`