inequalities

Question

If 0<x< 1 2 , which of the following statements must be true?
(A) 3+2x=4 (B) x<x2 (C) x>x2 (D) 2x>1 (E) x= x2 2

If 0<x<

1

2

, which of the following statements must be true?

     (A)  3+2x=4      (B)  x<x²      (C)  x>x²      (D)  2x>1      (E)  x=

x2

2

Answer 1

Using your fact that 0 < x < 1/2, the correct answer has to be (C)  x > x² is the answer that must be true.

 

I had to look at each answer choice and either solve for x or apply the rule from the inequality.  

If you apply the rule from the inequality and test a value between 0 and 1/2 in answer choice C, such as 1/4, you will see that is a true statement.

(1/4)² = 1/16  so we can conclude that

1/4 > 1/16 and this must be true for all x between 0 < x < 1/2.

 

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