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06 Dec 2014, 21:39
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Bookmarks
Check out Below two Posts to Understand Inequalities in bit more detail
How to Solve: Inequalities (Basic)
How to Solve: Inequality Problems - Algebra and Sine Wave/Wavy Method
Before the solution, I would like to tell you some theory
if we have x*y > 0 or x/y > 0 then that means that
both x and y can be either positive or both can be negative
i.e. both x and y have the same sign
so, we have
x>0, y>0 or x<0,y<0
if we have if you have x*y < 0 or x/y < 0 then that means that
(x can be positive and y will be negative) or (x can be negative and y will be positive)
i.e. x and y have opposite signs
so, we have
x>0, y<0 or x<0,y>0
Coming to the question
x*(x-1) > 0
this is of the form xy>0 i.e. x and y have the same sign
so,
(1) either, x > 0 and x-1 >0
i.e. x >0 or x>1
taking intersection of the two possibilities we have x >1
(2)or x <0, and x-1 < 0
i.e. x <0 or x<1
taking intersection of the two possibilities we have x < 0
So, solution will be x <0 or x>1
Hope it helps!
How to Solve: Inequalities (Basic)
How to Solve: Inequality Problems - Algebra and Sine Wave/Wavy Method
Before the solution, I would like to tell you some theory
if we have x*y > 0 or x/y > 0 then that means that
both x and y can be either positive or both can be negative
i.e. both x and y have the same sign
so, we have
x>0, y>0 or x<0,y<0
if we have if you have x*y < 0 or x/y < 0 then that means that
(x can be positive and y will be negative) or (x can be negative and y will be positive)
i.e. x and y have opposite signs
so, we have
x>0, y<0 or x<0,y>0
Coming to the question
x*(x-1) > 0
this is of the form xy>0 i.e. x and y have the same sign
so,
(1) either, x > 0 and x-1 >0
i.e. x >0 or x>1
taking intersection of the two possibilities we have x >1
(2)or x <0, and x-1 < 0
i.e. x <0 or x<1
taking intersection of the two possibilities we have x < 0
So, solution will be x <0 or x>1
Hope it helps!
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