`(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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