Question

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

Answer 1

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

Explanation:

We start from the equation:

`6-3|2x+6|=0`

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

`-3|2x+6|=-6`

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

`|2x+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|={(x,x>=0),(-x,x<0):}`

Using this definition we can write that:

`2x+6=2 vv 2x+6=-2`

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

`2x=-4 vv 2x=-8`

`x=-2 vv x=-4`