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10 Jan 2012, 18:01
Kudos
Bookmarks
Hi all,
This has been bugging me:
If I have:
x^2>x
I need some assurance on how to manipulate this...
I go:
x^2-x>0
x(x-1)>0
Here is where I start to get confused. I get 4 answers.
1. x>0
2. x-1>0
x>1
3. -x>0
x0
x1 for scenarios 1 + 2, and x<1 for scenarios 3+4?
And if this were a DS problem, if x falls into either of those 2 scenarios, it is SUFFICIENT?
This has been bugging me:
If I have:
x^2>x
I need some assurance on how to manipulate this...
I go:
x^2-x>0
x(x-1)>0
Here is where I start to get confused. I get 4 answers.
1. x>0
2. x-1>0
x>1
3. -x>0
x0
x1 for scenarios 1 + 2, and x<1 for scenarios 3+4?
And if this were a DS problem, if x falls into either of those 2 scenarios, it is SUFFICIENT?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
10 Jan 2012, 18:19
Kudos
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Hi, there. I'm happy to help with this. 
So, your algebra starts off great:
x^2>x
x^2-x>0
x(x-1)>0
At this point, we have to be very careful thinking about the mathematical logic.
If A*B > 0 that means (A > 0) AND (B > 0) OR (A < 0) AND (B < 0). The words "AND" and "OR" are not garnish here -- they are mathematical operators every bit as important as add, subtract, multiply, and divide.
If both factors of our algebra express are positive, we have:
x > 0 AND x - 1 > 0
Because we have a strict "AND" connection between those two statements, we have to take the overlap, the intersection, of the regions, which is x > 1. If x > 1, then both of the individual inequalities are satisfied.
If both factors are negative, then:
x < 0 AND x - 1 < 0
Again, a strict "AND" connection, so we take the intersection of the regions, which is x < 0. If x < 0, then both individual inequalities are satisfied.
Finally, joining those two solution is the operator "OR", so the complete solution is:
(x > 1) OR (x < 0)
That also corresponds to the graphical regions where the graph of y = x^2 is above the graph y = x.
Does that make sense? Please let me know if you have any questions on what I've done here.
Mike
So, your algebra starts off great:
x^2>x
x^2-x>0
x(x-1)>0
At this point, we have to be very careful thinking about the mathematical logic.
If A*B > 0 that means (A > 0) AND (B > 0) OR (A < 0) AND (B < 0). The words "AND" and "OR" are not garnish here -- they are mathematical operators every bit as important as add, subtract, multiply, and divide.
If both factors of our algebra express are positive, we have:
x > 0 AND x - 1 > 0
Because we have a strict "AND" connection between those two statements, we have to take the overlap, the intersection, of the regions, which is x > 1. If x > 1, then both of the individual inequalities are satisfied.
If both factors are negative, then:
x < 0 AND x - 1 < 0
Again, a strict "AND" connection, so we take the intersection of the regions, which is x < 0. If x < 0, then both individual inequalities are satisfied.
Finally, joining those two solution is the operator "OR", so the complete solution is:
(x > 1) OR (x < 0)
That also corresponds to the graphical regions where the graph of y = x^2 is above the graph y = x.
Does that make sense? Please let me know if you have any questions on what I've done here.
Mike
10 Jan 2012, 18:34
Kudos
Bookmarks
Mike,
Thanks so much!
This absolutely makes sense. Taking another look at this, I realized both terms (x and x-1) HAVE to have the same sign. I need to learn to take a step back and analyze the mathematical logic more often, rather than just plug and chug.
Awesome, thanks again!
Thanks so much!
This absolutely makes sense. Taking another look at this, I realized both terms (x and x-1) HAVE to have the same sign. I need to learn to take a step back and analyze the mathematical logic more often, rather than just plug and chug.
Awesome, thanks again!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
