1.

Solve `(x)/(x+2) le (1)/(|x|)`

Answer» `(x)/(x+2) le (1)/(|x|)`
`or (x|x|)/(x+2) le 1`
or ` (x|x|)/(x+2) le 1`
`or (x|x| - x- 2 )/(x+2) le 0`
Case (i) `x ge 0 `
or `((x^2)-x-2)/(x+2) le 0`
or `0 le x le 2 (as x ge 0)`
Case(ii) `x lt 0 `
`(-x^2-x-2)/(x+2) ge 0 `
`rArr -2 lt x lt 0 (as x^2 + x+2 gt 0 AA x in R, and x lt 0 )`
From (1) and (2) `x in (-2,2]`


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