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I got this, for x<0, 1/(-x)>-1, so when we multiply by -1 and flip signs,we get 1/x<1, so x>1.

Can you please explain how you got 1+x<0 for x<0. Please correct me. I am doing something wrong here. Is there any concept file to know more about inequalities? I was not able to find any chapter in GMATClub Maths book. Thanks in advance.

I got this, for x<0, 1/(-x)>-1, so when we multiply by -1 and flip signs,we get 1/x<1, so x>1.

Can you please explain how you got 1+x<0 for x<0. Please correct me. I am doing something wrong here. Is there any concept file to know more about inequalities? I was not able to find any chapter in GMATClub Maths book. Thanks in advance.

If x is negative, then x denotes negative quantity, no need to replace x with -x.