Question

Solve the following inequations
|x+2|/x<2
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Answer 1

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x+2∣x−1∣<1

(i)when(x−1)>0,x>1

x+2x−1<1

x+2x−1−x−2<0

x+2−3<0

x+21>0

xε(2,∞)

(ii)when(x−1)<0,x<1

x+2−x+1<0

x+21−x−x−2<0

x+2−2x−1<0

x+2x+21>0,xε(−∞,−2)⋃(2−1,∞)

when<1,xε(−∞,−2)⋃(2

Answer 2

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