Question

How do you solve and write the following in interval notation: `|x + 3| < 12`?

Answer 1

`-15<x<9` or `x in(-15,9)`

Explanation:

To solve this we have to understand what |x+3| means, namely the absolute value of (x+3). That means (x+3) must have a value between -12 and +12, so
`-12<(x+3)<12`
But for `-12<(x+3)` we must have `-15<x`.

And for `x+3<12` we must have `x<9`

Therefore it follows that `-15<x<9`.

Which also can be written as `x in(-15,9)`

Graphically