How can you tell what kind of compound inequality an absolute value inequality will represent?
If the absolute value inequality is of the form where the
absolute value of the difference between a variable (X) and some
constant (a) is compared to another constant (b)
eg |X - a| compared with b, then
if the comparison is < or ≤, the compound inequality is a
double inequality of the form c < X < d (or ≤),
and
if the comparison is > or ≥, the compound inequality is a
disjoint inequality of the form X < c or X > d (or including
the equals).
In both cases, c = b - a, d = b + a (>c)