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Solve: (-1)/(|x|-2)geq1,w h e r ex in R...

Solve: `(-1)/(|x|-2)geq1,w h e r ex in R ,x!=+-2.`

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The correct Answer is:
N/a
`(-1)/(|x|-2)ge1`
`rArr (-1)/(|x|-2)ge 0 `
`rArr (-1-|x|+2)/(|x|-2)ge0`
` rArr (1-|x|)/(|x|-2) ge0`
`rArr (|x|-1)/(|x|-2)leo`
` rArr (|x|-2ge0,|x|-2lt0)`
or `(|x|-1le 0, |x|-2gt0)`
`rArr (|x|ge1, |x|lt2) or (|x|le 1, |x|gt 2)`
But `|x|le 1, |x|gt 2` is not valid.
`:. |x|ge 1,|x|lt2`
`rArr 1le |x|lt2`
`rArr xin (-2,-1]cup [1,2).`
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