Your wording is confusing but I think I get your question. The "and" or "or" depends on where your answers lie.
For example, if you end up with x > 5, x < 9, you answer is x is greater than 5 and less than 9, because it is possible for your x-value to be both, take 6, for example.
On the contrary, if you end up with x < 5, x > 9, well your x-value can't be less than 5 and greater than 9. That's not happening! So, you have x < 5 or x > 9.
Now, I've thought more about your question. Absolute value is the distance from 0, which is always measured positively. If you have a less than sign, that means the distance has to be less than what's on the other side, right? The closer you get to 0 from either direction, the smaller the absolute value, so your function has to be an "and."
|5x - 1| < 9
Well, if the absolute value is less than 9, what's inside has to be less than 9 and greater than -9, right? You can't say "or" because 11 is less than 9 or greater than -9, but the absolute value of 11 is not less than 9!
A greater than would be the opposite. Your absolute value is getting larger as you move away from 0, so you are going to have an "or."
|5x - 1| > 9
Now, for the absolute value to be greater than 9, the inside has to be less than -9 or greater than 9, right? It can't be "and" because nothing is less than -9 AND greater than 9.
Hope this helps!
