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If 2le||x-2|-1|le3, then x belongs to in...

If `2le||x-2|-1|le3`, then `x` belongs to interval

A

`[-2, -1]uu[5, 6]`

B

`[-4, 6]`

C

`(-oo, -4]uu[6, oo]`

D

`[0, 1]uu[5,6]`

Text Solution

Verified by Experts

The correct Answer is:
A
If `2 le ||x-2|-1|le3` ………..
`2le||x-2|-1|le3`
(i) `|x-2|-1|ge2 or |x-2|-1le -2`
`x ge 5 , or , x le -1`
(ii) `le 3`
`-3 le |x-2|-1le3`
`-2le |x-2|le 4`
`|x-2|le4`
`-2le x le 6`
`(i)nn(ii) implies x epsilon [-2, -1]uu[5,6]`
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