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

1 Answer
Apr 1, 2018

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!