idreesma wrote:
Hi,
I am having issues with a fundanmental concept. In the below explanation x(x+1)>0 , isnt x>0 and x>-1 (from x+1>0) rather than x<-1 and x>0. clearly by inspection my answer is wrong, but was confused over how you go correct answer (is it possible to show the steps)
If x>0 then x2-x>0 --> x(x-1)>0 --> x<0 and x>1. Since we are considering x>0 range then x>1;
If x<0 then x2-x>0 --> x(x+1)>0 --> x<-1 and x>0. Since we are considering x<0 range then x<-1;
appreciate your input
Thanks
Responding to a pm:
The problem you are facing is that you do not know how to handle inequalities.
How do you get the range for which this inequality holds? x(x+1) > 0
Think of it this way: Product of x and (x+1) should be positive. When will that happen? When either both the terms are positive or both are negative.
Case 1: When both are positive
x > 0
x + 1 > 0 i.e. x > -1
For both to be positive, x must be greater than 0. Hence this inequality will hold when x > 0.
Case 2: When both are negative
x < 0
x + 1 < 0 i.e. x < -1
For both to be negative, x must be less than -1. Hence this inequality will hold when x < -1.
So we get two ranges in which this inequality holds: x > 0 or x < -1.
The fastest way to solve it is using the number line.
Check this post for the explanation of this method:
inequalities-trick-91482.htmlAlso, your
Veritas book discusses this concept too.
_________________
Karishma
Veritas Prep GMAT Instructor
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