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

2 Answers
Mar 13, 2018

The solution is x=1.

Explanation:

First, multiply both sides by 3. Then, add 6x to both sides. Lastly, divide both sides by 9. Here's how it looks:

1/3(9-6x)=x

color(blue)(3*)1/3(9-6x)=color(blue)(3*)x

color(red)cancelcolor(blue)3color(blue)\*1/color(red)cancelcolor(black)3(9-6x)=color(blue)(3*)x

1(9-6x)=color(blue)3x

9-6x=3x

9-6xcolor(blue)+color(blue)(6x)=3xcolor(blue)+color(blue)(6x)

9color(red)cancelcolor(black)(-6xcolor(blue)+color(blue)(6x))=3xcolor(blue)+color(blue)(6x)

9=3x+6x

9=9x

9color(blue)(div9)=9xcolor(blue)(div9)

1=9xcolor(blue)(div9)

1=x

That's the solution. Hope this helped!

Mar 13, 2018

x=1

Explanation:

A few ways, the simplest would be to first move the 1/3 to the other side so it becomes xx3. So now the equation is

9-6x=3x

Then move the -6x to the other side of the equals sign to make

9= 3x+6x

9=9x

Then divide both sides by 9 (take the 9x which is 9 multiplied by x back to the other side) to make

(9x)/9 = 9/9

x=1

Another way to do it is to actually divide the 9 and 6 by 3 since they are divisible making

3-2x=x

Using the same method above this would make

3=3x

Making x=1 again.