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# FP2 inequalities question watch

1. So I worked it out and have got it down to two possible sets of values :

,

,

Now , my textbook says the answer should be the second option. But how is it possible that a number be greater than -2 and less than -1?( and be less than -4!)
Isn't the first option the only one possible?
( Im not allowed to solve graphically)
2. (Original post by princejan7)

So I worked it out and have got it down to two possible sets of values :

,

,

Now , my textbook says the answer should be the second option. But how is it possible that a number be greater than -2 and less than -1?( and be less than -4!)
Isn't the first option the only one possible?
( Im not allowed to solve graphically)
Well the actual answer to what you've put is x > 2 or -4 < x < -1, which is neither of those. So, check your post and/or provide some working.
3. oh, my mistake.

So the two possible sets are

,

,

But I still dont understand why the second possibility is the answer..How can a number be between -1 and 2 and be less than -4?
4. (Original post by princejan7)
oh, my mistake.

So the two possible sets are

,

,

But I still dont understand why the second possibility is the answer..How can a number be between -1 and 2 and be less than -4?

What method are you using to solve these inequalities to check the regions?
5. How? I get x>-4 .
6. Its kind of a long working and im not too familiar with Latex but the idea is if

then either

or
7. (Original post by princejan7)
Its kind of a long working and im not too familiar with Latex but the idea is if

then either

or
I make it the other way around

then either

in which case x > -4 and [x < -1 or x >2] which leads to -4 < x < -1 or x > 2

or

in which case x < -4 and -1 < x < 2 which has no solutions.

So the nett result is -4 < x < -1 or x > 2
8. (Original post by ghostwalker)
I make it the other way around

then either

in which case x > -4 and [x < -1 or x >2] which leads to -4 < x < -1 or x > 2

or

in which case x < -4 and -1 < x < 2 which has no solutions.

So the nett result is -4 < x < -1 or x > 2
Why did you make it

Could you please post a similar working with <0?

Because i cant seem to get the required answer of x<-4, -1<x<2
9. (Original post by princejan7)
Why did you make it
Post how you're getting it the other way around, then someone can check where you're making the slip.
10. [QUOTE=ghostwalker;30736165]Post how you're getting it the other way around, then someone can check where you're making the slip.[/QCould you please post a similar working with >0?

x+4 > 0
x>-4

AND
(x+1)(x-2) < 0
x+1<0 x-2>0
x<-1 x>2
x+1>0 x-2<0
x>-1 x<2

So for this set , the result is x>-4 , -1<x<2

OR

x+4 < 0
x<-4

AND
(x+1)(x-2) > 0
x+1>0 x-2>0
x>-1 x>2
x+1<0 x-2<0
x<-1 x<2

And for this set, the result is x<-4 and x>2 or x<-1

The required answer of x<-4, -1<x<2 is a cross between them both..
11. (Original post by princejan7)

You've not said how you came to this part, and that is the bit that's wrong.
12. The correct inequality is as GW says: .
13. (Original post by ghostwalker)
You've not said how you came to this part, and that is the bit that's wrong.
Well, the original question was :

14. (Original post by princejan7)
Well, the original question was :

That's NOT what you put in your original post!
15. (Original post by ghostwalker)
That's NOT what you put in your original post!

sorry!!
wish i had typed it out properly at the beginning...
16. (Original post by princejan7)
sorry!!
wish i had typed it out properly at the beginning...
Me too!

(Original post by princejan7)

x+4 > 0
x>-4

AND
(x+1)(x-2) < 0
x+1<0 x-2>0
x<-1 x>2
x+1>0 x-2<0
x>-1 x<2

So for this set , the result is x>-4 , -1<x<2
What you've done here, is say "if the numerator is positive", i.e. if x > -4, then x lies between -1 and 2.

So -1 < x < 2 is part of the solution, as that is the overlap between x > -4 and -1 <x <2.

OR

x+4 < 0
x<-4

AND
(x+1)(x-2) > 0
x+1>0 x-2>0
x>-1 x>2
x+1<0 x-2<0
x<-1 x<2

And for this set, the result is x<-4 and x>2 or x<-1

The required answer of x<-4, -1<x<2 is a cross between them both..
And here you have "if the numerator is negative", i.e. x < -4, then it is > 2 or < -1.

And the restriction becomes x < -4, as that is the overlap between the two intervals.

And hence your final solution is x < -4 or -1 < x < 2

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