Question

How do you solve `\frac { 1 } { 2 } ( - 4 + 6 x ) = \frac { 1 } { 3 } x + \frac { 2 } { 3 } ( x + 9 )`?

Answer 1

x=4

Explanation:

First, use distributive property on the `(1/2)(-4+6x)` and `(2/3)(x+9)`.

`(1/2)(-4+6x) = (1/2)*-4+(1/2)*6x = -2+3x`
`(2/3)(x+9) = (2/3)*x+(2/3)*9 = 2/3x+6`

The equation is now `-2+3x=1/3x+2/3x+6`.

Combine like terms and make it "prettier".

`3x-2=x+6`.

Now we've broken it down into something much more simple!

Subtract `6` from both sides to get
`3x-2-6=x+6-6 => 3x-8=x`

Subtract `x` from both sides to get
`3x-x-8 = x-x => 2x-8=0`

Add `8` to both sides to get
`2x-8+8=0+8 => 2x=8`

Final step: Divide `2` from both sides to get
`2x/2=8/2 => x=4`

Therefore, `x=4`.

Yay!