Question

How do you solve `4x + 2( 8- 3x ) = 12x`?

Answer 1

`x = 8/7`

Explanation:

Ok first you need to get the `x`'s on to one side and the numbers on their own on the over, so first expanding the bracket you get

`4x + 16 - 6x =12x`

Once we collect like terms we end up with

`-2x +16 = 12x`

Now what we do to one side, we do to the other, so if we add `2x` to get rid of the `-2x`, we have to also add `2x` to the `12` so we end up with

`16=14x`

And supposedly you want just `x`, so we have to divide both sides by `14`, which is

`x = 16/14 = 8/7 ~~ 1.4286`

Answer 2

Simplify the expression, rearrange terms, and then solve to find `x=8/7`

Explanation:

First, we'll simplify. We could multiply both the terms that are in the parentheses by the coefficient (2), but note that the other terms outside of the parentheses are divisible by 2. For this, I elected to divide both sides by 2, which eliminates the need for the parentheses:

`(4x+2(8-3x))/2=(12x)/2`

`2x+(8-3x)=6x`

`2x+8-3x=6x`

Next, we'll combine like terms:

`8+x(2-3)=6x`

`8-x=6x`

Next, we rearrange by adding `x` to both sides:

`8cancel(-x)color(red)(cancel(+x))=6xcolor(red)(+x)`

`8=x(6+color(red)(1))`

`8=7x`

Finally, we divide through by `x`'s coefficient:

`8/color(red)(7)=(cancel(7)x)/color(red)(cancel(7))`

`color(green)(x=8/7~=1.1429`