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Solve `|1-(|x|)/(1+|x|)| ge 1/2`

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Solve `|1-(|x|)/(1+|x|)| ge 1/2`
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Correct Answer - `-1 le x le 1`
|1-(|x|)/(1+|x|)|ge 1/2
or `|1/(1+x|x|)|ge1/2`
or 1+|x|le2`
or `|x|le 2 `
`-1 le x le 1`
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