Find the range of values of x for which \(\frac{1}{x}\) > 2 is true

A.

x < \(\frac{1}{2}\)

B.

x < 0 or x < \(\frac{1}{2}\)

C.

0 < x < \(\frac{1}{2}\)

D.

1 < x < 2

Correct answer is C

\(\frac{1}{x}\) > 2 = \(\frac{x}{x^2}\) > 2

x > 2x2

= 2x2 < x

= 2x2 - x < 0

= x(2x - 10 < 0

Case 1(+, -) = x > 0, 2x - 1 < 0

x > 0, x < \(\frac{1}{2}\) (solution)

Case 2(-, 4) = x < 0, 2x - 1 > 0

x < 0, x , \(\frac{1}{2}\) = 0