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Solve (1)/(|x|-3) lt 1/2...

Solve `(1)/(|x|-3) lt 1/2`

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The correct Answer is:
` x in (-oo ,5 ) cup (-3 , 3) cup (5,oo)`
`(1)/(|x|-3)-1/2 lt 0`
`or (2-|x|+3)/(|x|-3) lt 0 `
`or (|x|-5)/(|x|-3) gt 0 `
`rArr |x| gt 5 or |x| lt 3`
` rArr x lt 5 or x lt -5 or -3 lt x lt -3`
`rArr x in (-oo , -5)cup(-3,3) cup (5,oo)`
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