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This problem trains for: SAT-I, AMC-8, GMAT.

If the following is always true:

equation

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:

equation

which means that:

equation

and

equation

and the true answer choices are now obvious (I and IV).