# Question #be18e

Dec 7, 2017

The solution is "All Real Numbers."

#### Explanation:

First let's distribute on the left side:

$3 \left(x - 6\right) = 3 x - 18$

On the left side, we now have $3 x - 18 - x$. Combine like terms now. $x$ is the only like term on the left side.

$3 x - x = 2 x$ and $- 18$ stays the same. Therefore we now have:

$2 x - 18 = 4 x - 2 \left(x + 6\right)$.

We now need to distribute the $- 2$ on the right side to what's in the parenthesis. Do the following:

$- 2 \left(x + 9\right) = - 2 x - 18$

Combine like terms once again. As with the left side, the only like term is the $x$ value:

$4 x - 2 x = 2 x$. The $- 18$ stays the same.

Now that we've simplified both sides, we can work with the equation, finally. When simplified we get:

$2 x - 18 = 2 x - 18$

Notice how they are equivalent values. This means any value plugged into this system will result in the same value on the left and right sides. Always. Therefore, this equation has infinite solutions for real numbers.

Solution: All Real Numbers

I hope that helps!