# How do you solve 6 - 3|2x + 6| = 0?

Jul 16, 2016

This equation has 2 solutions: $- 4$ and $- 2$

#### Explanation:

We start from the equation:

## $6 - 3 | 2 x + 6 | = 0$

First we move number $6$ on the right side:

## $- 3 | 2 x + 6 | = - 6$

Now we can divide both sides by $- 3$:

## $| 2 x + 6 | = 2$

Now we can change the equation with absolute value to 2 equations without absolute value. To do this we use the definition of absolute value:

## $| x | = \left\{\begin{matrix}x & x \ge 0 \\ - x & x < 0\end{matrix}\right.$

Using this definition we can write that:

## $2 x + 6 = 2 \vee 2 x + 6 = - 2$

Now we have to solve the two equations to get the final answer: