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If |x-1|+|x+1|=2, then find x....

If `|x-1|+|x+1|=2`, then find x.

A

`-2 lexle1`

B

`x= -1, 1`

C

`-1 lexle1`

D

`-1 lexle2`

Text Solution

Verified by Experts

The correct Answer is:
C
Case-I: If `xle-1`
`-(x-1)-(x+1)=2`
`rArr -x+1-x+1=2`
`rArr -2x=2 rArr x=-1`…………(i)
Case(ii): If `-1 lt x lt 1`
`-(x-1)+9x+1=2`
`rArr -x+1+x+1=2`
`rArr 2=2 rArr -1 lt x lt 1`…………..(ii)
Case iii): If `x ge1`
`x-1+x+1=2`
`rArr x=1`...................(iii)
Thus, from (i), (ii) and (iii) `-1 lexle1`
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