about intervals

[gh0st]

http://www.math.ucdavis.edu/~marx/rtinequalPr/rtinequalPr.html


on pr5 I find the factors but when i do the sign charts it takes me too long i think there is a way to do it faster just by selecting pair and unpair values of X but i dont remember it much fuck! or maybe my brain is lying me is a fake memory plz dont post trash thank y 

[gh0st]

k all values of X are impairs some shit like that so I can + , - , + , - but whats the name of that rule so I can do some research ayn1?

[gh0st]

guys im stuck on this help idk how to put + or -

[Deque]

I don't really know what your are asking (I have difficulties understanding some mathematical terms that are not my mothertongue, i.e. what are impairs?)

But I guess you want rules for factorization like:
a²-b² = (a+b)(a-b)
?

You find some of them here:
https://en.wikipedia.org/wiki/Factorization

[gh0st]

the problem is in this website it would be problem number 4 http://www.math.ucdavis.edu/~marx/rtinequalPr/rtinequalPr.html

and solutions here
http://www.math.ucdavis.edu/~marx/rtinequalSol/rtinequalSol.html
why do they start with - and not with +.

[Deque]

the problem is in this website it would be problem number 4 http://www.math.ucdavis.edu/~marx/rtinequalPr/rtinequalPr.html

and solutions here
http://www.math.ucdavis.edu/~marx/rtinequalSol/rtinequalSol.html
why do they start with - and not with +.

You have to calculate y with a sample value for x (doesn't matter which value, but it shouldn't be a root).
They did it for x=0. The result was negative, so the interval that contains 0 is negative (that's (-2, 5/2)).
Once you know the sign of one intervall, you also know the others.

[Mordred]

Well look at the equation that he obtained. Luckily he is able to divide the fraction in such a way so that you have only multiplications, which alleviates the biggest problem (in the future you won't be able to do that anymore: polynomial functions etc).

Your fraction is (2x-5)(x+2)/(4-x)(3+x) > 0

x cannot be 4 or -3 otherwise the fraction doesn't make sense (DIVIDE BY ZERO BRAH!)

You ask why the start with a minus, so let's see the reasoning:

assume x = -4;
input into equation => [2*(-4)-5]*[(-4)+2]/[4-(-4)]*[3+(-4)] > 0 => (-8-5)*(-4+2)/(4+4)*(3-4) > 0
=> -13*(-2)/8*(-1) > 0 => 26/-8 > 0 False; 

Because the result doesn't make mathematical sense, and you want it to (the solution is always in the "+" intervals), it means that you can't find a root in the specific interval, which in this case is [-infinity;-3).

Now since solution intervals are positive, non-solution intervals must be negative, and (-infinity;-3] has no value which correctly solves the inequation.

As Deque correctly said, it's sometimes difficult to translate mathematical concepts from mother-tongue to English, but I hope you get what I mean.

[Snayler]

Shouldn't it be ]-infinity,-3]?
                     ^

[Deque]

Shouldn't it be ]-infinity,-3]?
                     ^

You are right.
Maybe Mordred confused the notation. (a,b) is an open interval, [a,b] is closed

[Snayler]

You are right.
Maybe Mordred confused the notation. (a,b) is an open interval, [a,b] is closed

I've learned it like this: [a,b] is closed, ]a,b] is open in the lower limit, [a,b[ open in the higher limit, ]a,b[ when the interval is open on both sides. For example, ]-3, 5[ means the interval has numbers from -3 to 5, excluding -3 and 5.
I'm European, don't know if that explains the differences.

[Deque]

It is just another notation. Both are used and valid.

[Mordred]

Shouldn't it be ]-infinity,-3]?
                     ^

Just a typo in my post. It should be (-infinity;-3] (at least for my version of European notations  )

[gh0st]

You have to calculate y with a sample value for x (doesn't matter which value, but it shouldn't be a root).
They did it for x=0. The result was negative, so the interval that contains 0 is negative (that's (-2, 5/2)).
Once you know the sign of one intervall, you also know the others.

thanks for the responses

i totally understand but when we have lots factors isnt there a fastest way to search for + and - sections? i think that they are just adding +,-,+,-,+,-,+ if it fits into a condition but Im not sure or are they replacing and finding out what to put?

[Deque]

thanks for the responses

i totally understand but when we have lots factors isnt there a fastest way to search for + and - sections? i think that they are just adding +,-,+,-,+,-,+ if it fits into a condition but Im not sure or are they replacing and finding out what to put?

That is the fastest way. Make up an easy to calculate value for x. Then you know the sign of one section and that is enough to know all the others, because the curve crosses the x-axis at those points. So when you discovered the middle section to be -, the section right and left form it are + and so on.

[gh0st]

That is the fastest way. Make up an easy to calculate value for x. Then you know the sign of one section and that is enough to know all the others, because the curve crosses the x-axis at those points. So when you discovered the middle section to be -, the section right and left form it are + and so on.

that makes totally sence!!!    thank you!