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Find the range of values of x for which $\frac{1}{x}$ > 2 ...

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

View answer & explanation

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

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