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Transitive Property

If x < y and y < z, then x < z
 
Example

If 1/Q > 1, which of the following must be true?

  1. 1 < Q2
  2. 1 > Q2
  3. Q < Q2
Solution
Since 1/Q > 1 and 1 > 0, we know from the transitive property that 1/Q is positive.
Hence, Q is positive. Therefore, we can multiply both sides of 1/Q > 1 by Q without reversing the inequality:
Reducing yields 1 > Q
Multiplying both sides again by Q yields Q > Q2
Using the transitive property to combine the last two inequalities yields 1 > Q2
The answer is (C).
 





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