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# FP2 Inequalities solutions help Watch

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1. Can anyone explain to me how to determine the inequality solutions of a graph?

I only know how to deal with two critical values which was from C1 but for 3 or more critical values I'm confused. The text book isn't very clear on this in my opinion.

(I know how to get the critical values of , I just put the full solution for those asking what the question is).

For example, the solution in the graph above is or . Why isn't it for example?

Any help is much appreciated
2. We found that . This means the acceptable intervals are where the function is above the -axis. This occurs where and .

For , the function is below the -axis, which isn't what we want.
3. (Original post by Desmos)
We found that . This means the acceptable intervals are where the function is above the -axis. This occurs where and .

For , the function is below the -axis, which isn't what we want.
Oh ok I get it now, thanks for your time
4. (Original post by ManLike007)
Oh ok I get it now, thanks for your time
Do you understand why they multiplied through by (x - 2)^2 instead of just (x - 2)? And how would you do the Q in the latter case?
5. (Original post by Physics Enemy)
Q: Do you understand why they multiplied through by (x - 2)^2 instead of just (x - 2)? And how would you do the Q in the latter case?
It's to do with getting a positive value (something like that) but I'm not quite sure if I'm being honest
6. (Original post by ManLike007)
It's to do with getting a positive value (something like that) but I'm not quite sure if I'm being honest
Sort of. is always positive on its natural domain unlike so when you multiply through by it, you don't need to flip the inequality sign or debate which way it would be since multiplying by a negative flips the sign always - this is clearly avoided by , or any other even power.

If you mult by then you'd need to consider two cases where and
7. (Original post by RDKGames)
Sort of. is always positive on its natural domain unlike so when you multiply through by it, you don't need to flip the inequality sign or debate which way it would be since multiplying by a negative flips the sign always - this is clearly avoided by , or any other even power.

If you mult by then you'd need to consider two cases where and
Oh right, that sounds reasonable. It makes sense now, thanks.

One more question I have, why do we take the interval above the x axis when the equation is >0 and the interval below the x axis when the equation is <0. Is there a particular reason for this?
8. (Original post by ManLike007)
Oh right, that sounds reasonable. It makes sense now, thanks.

One more question I have, why do we take the interval above the x axis when the equation is >0 and the interval below the x axis when the equation is <0. Is there a particular reason for this?
Because if you say on the xy plane then is the same as saying , and this is above the x-axis of course. Likewise for .
9. (Original post by RDKGames)
Because if you say on the xy plane then is the same as saying , and this is above the x-axis of course. Likewise for .
Ahh ok I get it, thanks for your time!

EDIT: Never really got a deeper understanding of inequalities in C1 (Edexcel) because it was a small topic (so you could get full marks without knowing much what was going on) so apologies for these silly questions
10. (Original post by ManLike007)
Ahh ok I get it, thanks for your time!

EDIT: Never really got a deeper understanding of inequalities in C1 (Edexcel) because it was a small topic (so you could get full marks without knowing much what was going on) so apologies for these silly questions
Even if you get away with it, inequalities/transformations are worth inspecting.

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