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FP2 Inequalities solutions help Watch

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    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 x=0, 2, 5, I just put the full solution for those asking what the question is).

    Name:  fp2 inequality.jpg
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    For example, the solution in the graph above is x<0 or 2<x<5. Why isn't it 0<x<2 for example?

    Any help is much appreciated
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    We found that x(x-2)(5-x) > 0. This means the acceptable intervals are where the function is above the x-axis. This occurs where  x < 0 and 2 < x < 5.

    For 0 < x < 2, the function is below the x-axis, which isn't what we want.
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    (Original post by Desmos)
    We found that x(x-2)(x-5) > 0. This means the acceptable intervals are where the function is above the x-axis. This occurs where  x < 0 and 2 < x < 5.

    For 0 < x < 2, the function is below the x-axis, which isn't what we want.
    Oh ok I get it now, thanks for your time
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    (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?
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    (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
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    (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. (x-2)^2 is always positive on its natural domain unlike (x-2) 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 (x-2)^2, or any other even power.

    If you mult by x-2 then you'd need to consider two cases where x \geq 2 and x<2
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    (Original post by RDKGames)
    Sort of. (x-2)^2 is always positive on its natural domain unlike (x-2) 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 (x-2)^2, or any other even power.

    If you mult by x-2 then you'd need to consider two cases where x \geq 2 and x<2
    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?
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    (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 y=f(x) on the xy plane then f(x)&gt;0 is the same as saying y&gt;0, and this is above the x-axis of course. Likewise for f(x)&lt;0.
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    (Original post by RDKGames)
    Because if you say y=f(x) on the xy plane then f(x)&gt;0 is the same as saying y&gt;0, and this is above the x-axis of course. Likewise for f(x)&lt;0.
    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
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    (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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