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|x-1|le5,|x|ge 2...

`|x-1|le5,|x|ge 2`

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`|x-1| le5`
`rArr -4 le x-1 le 5 `
`rArr -4 le x le 6 `
`rArr x in [-4, 6]` ….(i)

and `|x|ge2`
and `|x|ge2`
`rArr x le -2 or x ge 2 `
`rArr x in (- infty, -2] cup[2, infty) ..(ii)`

On combining Eqs. (i) and (ii), we get
`x in (4, -2] cup[2, 6]`
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