Question

Solve the inequality |3x+6|<12

Answer 1

I'm probably late but your a swer is _6

Answer 2

`-6<x<2`

Explanation:

We have the inequality
`|3x+6|<12`

In order to remove the absolute values, we need to add a ± to the opposite side of the equation. For ease of solving, I will split it up.

As we are multiplying one of the inequalities by a -1 when we are splitting up the ±, we will have to swap the inequality sign.

We now have two inequalities
`3x+6<12` and
`3x+6>-12`

Now we can solve for x for each of them.

`3x+6<12\\\\3x<6\\\\x<2`

And the second

`3x+6>-12\\\\3x>-18\\\\x>-6`

Now, we can combine our two answers

`-6<x<2`