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The solution set of the inequlity (|x-2|...

The solution set of the inequlity `(|x-2|-x)/(x)lt2 ` is

A

1.(0,1)

B

2.[0,2]

C

3.`(-oo,0) cup (1,oo)`

D

4.None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have `(|x+2|-x)/(x) lt 2 `
`rArr (|x+2|-3x)/(x)lt 0 `
Let `|x+2|-3x=0 `
`rArr x+2=pm 3x `
`rArr x=1`
sign scheme of the expression `(|x+2|-3x)/(x)` is as shown in the following figure :

From the sing scheme `x in (-oo,0) cup (1,oo)`
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