Consider an absolute value inequality.
For example, 3≤|x-7|
this means that x-7 can be
i) 3, 3.4, 5, 7.5 etc
or ii) -3, -3.2, -4.7 etc since these values in abs value all are ≥3
thus the set of all values in i) is represented by x-7≥3, which means x≥10
and the set of all values in ii) is x-7≤-3, which means x≤4.
Thus, the compound inequality is : x≥10 OR x≤4
an absolute inequality corresponding to this compound inequality is 3≤|x-7|