Question

How do you solve `|x - 9| + 3< 15`?

Answer 1

`-3<x<21`

Explanation:

First, we isolate`|x-9|` .
Therefore, `|x-9|+3<15` now becomes `|x-9|<12`.
Now, we ask ourselves: is the variable side larger or the number side?

If the variable side is larger, that means the answer to this inequality is a disjunction.

If the number is larger, that means the answer is a conjunction.

Since the number side is larger, we know that this is a conjunction. Therefore, we now have `-12<x-9<12`
We add 9 to all of them to get:
`-3<x<21`
That is our answer!