B  |2x-1| < -3  has an empty solution set because absolute 
values are never negative, and for the absolute value |2x-1| 
to be less than -3 it would have to be negative, which is 
impossible.

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[Some people might think D |2x-1| ≤ 0 would be the answer
but it isn't because even though |2x-1| can't be less than 0 it 
can be EQUAL to 0 and ≤ says "less than OR EQUAL 0", so it
CAN equal 0. Thus D is not the answer.]

Edwin