यदि `(x-1)/(2) ge 2`, तब `x in`

Options

A. (1, 2)
B. (0, 1)
C. `[5, oo)`
D. `(1, oo)`

Answer

C

Explanation

We have,
`(x-1)/(x) ge 2 rArr (x-1)/(2)-2 ge 0 rArr (-1-x)/(x) ge 0 rArr (x+1)/(x-0) le 0 " "…(i)`
On equating x +1 and x-0 to zero, we obtain x = -1 and x = 0 as critical points. These points when plotted on number line divide it into three regions. Marking alternatively positive and negative from the right most region, we obtain the signs of `(x+1)/(x)` for different values of x as shown in the following figure.
Since the expression in (i) is non-positive. So, the solution set of inequation (i) is [-1, 0].