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