inequalities - edexcel C1 - plz help Watch

sandra
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#1
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QUESTION:


a) solve the inequality
x^2 + 3x – 10 > 0



ANS: x < -5 or x >2



b) Find the set of values of x which satisfy both of thefollowing inequalities

x^2 + 3x – 10 > 0 and 3x – 2 < x +3


ANS:
3x – 2 < x + 3
Therefore x < 5/2

Both are satisfied when x < -5 or 2 < x < 5 /2



i dont understand how they get the line that is written in bold

can someone plz explain the concept/method to me?

thanks
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henryt
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OK. I think if you drew a numberline it would make things easier to visualise. Anyhow, basically, you've got to find where the regions of the inequalities overlap. And we know the largest number can only be 5/2, since if it went above this, even though it would still be fine for the first inequality, it would not work for the second. We know the smallest positive number has to be 2, because of the first equation. We also know that x can be less than -5, and because this doesn't clash with the region x<5/2 , we can accept it.

As a result, we get x < -5 or 2 < x < 5 /2 !

Does that help?
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sandra
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(Original post by henryt)
OK. I think if you drew a numberline it would make things easier to visualise. Anyhow, basically, you've got to find where the regions of the inequalities overlap. And we know the largest number can only be 5/2, since if it went above this, even though it would still be fine for the first inequality, it would not work for the second. We know the smallest positive number has to be 2, because of the first equation. We also know that x can be less than -5, and because this doesn't clash with the region x<5/2 , we can accept it.

As a result, we get x < -5 or 2 < x < 5 /2 !

Does that help?

sorry, but i still dont understand
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CalculusMan
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For the first inequality,

If you draw the curve x^2 + 3x – 10, which can be nicely factorised into (x + 5)(x - 2), you will see that the curve crosses the x axis at (-5, 0) and (2, 0)

Inequality is looking for when the curve is greater than 0 (y value greater than 0).

You will see on the graph that this is when x < -5 and when x > 2

EDIT: Damn, that wasn't the question asked.
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henryt
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I've drawn a numberline (You should be familiar with these from GCSE ): The red regions are where they overlap, and so the where both inequalities are solved! I hope this makes it clearer.
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sandra
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(Original post by henryt)
OK. I think if you drew a numberline it would make things easier to visualise. Anyhow, basically, you've got to find where the regions of the inequalities overlap. And we know the largest number can only be 5/2, since if it went above this, even though it would still be fine for the first inequality, it would not work for the second. We know the smallest positive number has to be 2, because of the first equation. We also know that x can be less than -5, and because this doesn't clash with the region x<5/2 , we can accept it.

As a result, we get x < -5 or 2 < x < 5 /2 !

Does that help?
i understood x<-5 but for the second one ( 2<x<5/2) ??
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henryt
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Did you look at my post above with the numberline? Hopefully that should clear it up!
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sandra
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(Original post by henryt)
I've drawn a numberline (You should be familiar with these from GCSE ): The red regions are where they overlap, and so the where both inequalities are solved! I hope this makes it clearer.

thanku soooooooo much henryt-that diag made things a lot clearer for me!

i now feel incredibly silly for having having asked an incredibly silly question!
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henryt
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That's alright - just as long as you understand it
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