SOLUTION: If xy > 1 and z < 0, which of the following statements must be true? I. x > z II. xyz < -1 III. xy/z

SOLUTION: If xy > 1 and z < 0, which of the following statements must be true? I. x > z II. xyz < -1 III. xy/z < 1/z

Question 308695: If xy > 1 and z < 0, which of the following statements must be true?

I. x > z
II. xyz < -1
III. xy/z < 1/z

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I. False. For example, let x = -10 and z = -1. Clearly is false. If we let , then showing that is true.

II. False, this is only true if . So is on the right track, but it is false. For example, if , and we let , then which is clearly not less than -1. We must make the requirement that the right side be 'z' and not -1.

III. This is true since dividing both sides of an inequality by a negative number will flip the inequality sign. Basically, divide both sides of by the negative number 'z' to get (don't forget to flip the sign).
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