Question

How can you tell what kind of compound inequality an absolute value inequality will represent?

Answer 1

this is a bit abstract, but perhaps you mean this:
if you have
\[|\text{something}|<p\] (less than) then you get
\[-p<\text{something}<p\] one compound inequality, an AND statement
whereas if you have
\[|\text{something}|>p\](greater than) then you get two separate inequalities
\[\text{something}<-p\] OR
\[\text{something}>p\]