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(|x+2|-x)/x

(|x+2|-x)/x<2 solve eq

Grade:Upto college level

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

dear akash

(|x+2|-x)/x<2

case 1 x<-2

so (-(x+2)-x)/x < 2

 (-2x -2)/x <2

 or (x+1)/x  > 1

     1+ 1/x  >1

  or  1/x >0 

  since x<-2 so no solution is possible

case -2 ≤x <0

so now

((x+2)-x)/x<2

 2/x <2

  1/x<1

   since lest side is negative so it is valid for all value   -2 ≤x <0

case 3   x≥0

so

((x+2)-x)/x<2

  2/x <2

 x>1

  so solution is possible for x>1

so final solution     -2 ≤x <0    and  x>1

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Badiuddin

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