Finding the set of u such that

[1question]

Hi. I'm having trouble understanding the logic behind finding a set of u for u(u-1) > 0. To solve these, I tend to factor as much as possible, then equate each expression to 0 (in this case to > 0) and solve, changing the > to < if I must divide by a negative number. I get u >0 and u > 1 but the solution is given as (-∞,0)U(1,∞), aka u>1 and u<0. Why does it say u<0?
Any help would be appreciated.

SOLVED. See below replies + http://tutorial.math.lamar.edu/Classes/Alg/SolvePolyInequalities.aspx

 

[Mark44]

Hi. I'm having trouble understanding the logic behind finding a set of u for u(u-1) > 0. To solve these, I tend to factor as much as possible, then equate each expression to 0 (in this case to > 0) and solve, changing the > to < if I must divide by a negative number.

This is not the correct approach. If u(u - 1) > 0 then either
1) u > 0 AND u - 1 > 0. This leads to u > 0 AND u > 1, which simplifies to u > 1
OR
2) u < 0 AND u - 1 < 0. This leads to u < 0 AND u < 1, which simplifies to u < 0

I get u >0 and u > 1 but the solution is given as (-∞,0)U(1,∞), aka u>1 and u<0.

No, (-∞, 0) U (1, ∞) does not mean u > 1 and u < 0, which no number can satisfy. There is no number that is simultaneously greater than 1 and negative.

(-∞, 0) U (1, ∞) means u < 0 or u > 1. The difference between "and" and "or" here is very significant.

Why does it say u<0?

See above

 

[1question]

Hi Mark. OK, I generally understand the idea, except for why you would do 2) in the first place. The sign is > not <, so why did you do both? Thanks.

EDIT: I believe I understand the process now.
http://tutorial.math.lamar.edu/Classes/Alg/SolvePolyInequalities.aspx is very helpful.

 

[Mark44]

Hi Mark. OK, I generally understand the idea, except for why you would do 2) in the first place. The sign is > not <, so why did you do both? Thanks.

Because if a*b > 0, either both numbers have to be positive or both have to be negative. For example (-2)(-4) = + 8.

EDIT: I believe I understand the process now.
http://tutorial.math.lamar.edu/Classes/Alg/SolvePolyInequalities.aspx is very helpful.

 

[Spring]

Alright, so what you have here Is fun.
in fact when you open the parentheses you will get: u² - u > 0.

Now to know when that happends you can simply solve what it should look like.
since the u^2 has a positive feature you can infer it will be a "smiling" parabule.
and you can clearly see the u(u-1) You can easly infere that the whole equation will equel zero at u=0 or u=-1

look at wolf ram alpha and see the discription fits.

After this you need to look at where the Y axis (the actual u(u-1)) is larger then 0.
You will find it does at numbers higher then 1 or lower then 0.

You're approax is deviding it into 2 separate the inequalities and I believe this way is easier and quicker.

Tell me if I am unclear.

 

[1question]

@ Spring. I figured it out already thanks to the link posted above. I appreciate the reply though!