Find the range of values of x for which \(\frac{1}{x}\) > 2 is true
- x < \(\frac{1}{2}\)
- x < 0 or x < \(\frac{1}{2}\)
-
0 < x < \(\frac{1}{2}\)
- 1 < x < 2
The correct answer is: C
Explanation
\(\frac{1}{x}\) > 2 = \(\frac{x}{x^2}\) > 2x > 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