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

Mar 13, 2018

The solution is $x = 1$.

#### Explanation:

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

$\frac{1}{3} \left(9 - 6 x\right) = x$

$\textcolor{b l u e}{3 \cdot} \frac{1}{3} \left(9 - 6 x\right) = \textcolor{b l u e}{3 \cdot} x$

$\textcolor{red}{\cancel{\textcolor{b l u e}{3}}} \textcolor{b l u e}{\setminus} \cdot \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} \left(9 - 6 x\right) = \textcolor{b l u e}{3 \cdot} x$

$1 \left(9 - 6 x\right) = \textcolor{b l u e}{3} x$

$9 - 6 x = 3 x$

$9 - 6 x \textcolor{b l u e}{+} \textcolor{b l u e}{6 x} = 3 x \textcolor{b l u e}{+} \textcolor{b l u e}{6 x}$

$9 \textcolor{red}{\cancel{\textcolor{b l a c k}{- 6 x \textcolor{b l u e}{+} \textcolor{b l u e}{6 x}}}} = 3 x \textcolor{b l u e}{+} \textcolor{b l u e}{6 x}$

$9 = 3 x + 6 x$

$9 = 9 x$

$9 \textcolor{b l u e}{\div 9} = 9 x \textcolor{b l u e}{\div 9}$

$1 = 9 x \textcolor{b l u e}{\div 9}$

$1 = x$

That's the solution. Hope this helped!

Mar 13, 2018

$x = 1$

#### Explanation:

A few ways, the simplest would be to first move the $\frac{1}{3}$ to the other side so it becomes $\times 3$. So now the equation is

$9 - 6 x = 3 x$

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

$9 = 3 x + 6 x$

$9 = 9 x$

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

$\frac{9 x}{9} = \frac{9}{9}$

$x = 1$

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

$3 - 2 x = x$

Using the same method above this would make

$3 = 3 x$

Making $x = 1$ again.