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This problem trains for: SAT-I, AMC-8, GMAT.
If the following is always true:
then which one of the following MUST be true:
Since the expression is a sum of two absolute values, its minimum (least possible) value is 0 and it occurs only when both absolute values are 0.
The expression is equivalent to:
which means that:
and the true answer choices are now obvious (I and IV).