Question

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

Answer 1

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!

Answer 2

`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.