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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

If:

is true, then which one(s) of the following statements are also true?

The absolute value inequality is equivalent to the system of two inequalities:

Subtract p from both sides:

and multiply all by -1 (this will flip the inequalities!):

to get II.

Going back to:

add q to both sides to get:

which is the identical to III.

The other two choices cannot be related to the original inequality using algebraic manipulation.