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Math Help - Solving equations #2

  1. #1
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    Red face Solving equations #2

    Hi i need some help please on how to solve these problems. i tried each one but either cant figure out the answer/ i got an answer but im not sure if its correct.

    1) Use an absolute value inequality to describe te numbers that are between -6 and 8 insclusively.

    -So for this problem i believe its just asking us to write down/ translate the sentence. This is what i got.

    -6 < x < 8

    only thing is im not sure if thats correct or if this is what im suspose to do...


    2)Factor completely. x^9/5 -4x^4/5 -5x^-1/5

    for this i took the smallest exponet fraction which was -1/5 and got.

    -x^-1/5 (x^-9 +4x^-4 +5)

    after i did this i couldnt see anything else i could do to factor it out even more. Then again im not the best with fraction exponets.....

    help would be much appreciated! thanks!
    Last edited by mr fantastic; January 29th 2011 at 01:55 PM.
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  2. #2
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    Quote Originally Posted by Nismo View Post
    1) Use an absolute value inequality to describe te numbers that are between -6 and 8 insclusively.
    If a<x<b you can express that as \left|x-\frac{b+a}{2}\right|<\frac{b-a}{2}.
    Last edited by mr fantastic; January 29th 2011 at 01:55 PM.
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  3. #3
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    Red face

    Quote Originally Posted by Nismo View Post
    Hi i need some help please on how to solve these problems. i tried each one but either cant figure out the answer/ i got an answer but im not sure if its correct.

    1) Use an absolute value inequality to describe te numbers that are between -6 and 8 insclusively.

    -So for this problem i believe its just asking us to write down/ translate the sentence. This is what i got.

    -6 < x < 8

    only thing is im not sure if thats correct or if this is what im suspose to do...


    2)Factor completely. x^9/5 -4x^4/5 -5x^-1/5

    for this i took the smallest exponet fraction which was -1/5 and got.

    -x^-1/5 (x^-9 +4x^-4 +5)

    after i did this i couldnt see anything else i could do to factor it out even more. Then again im not the best with fraction exponets.....

    help would be much appreciated! thanks!
    For 1 your answer is incorrect. It does not use an absolute value.

    It should look like |x-a|<b where a and b are real numbers.
    Hint let a be the midpoint of the interval

    For 2: you have factored incorrectly
    Hint:
    \displaystyle  x^{\frac{9}{5}}-4x^{\frac{4}{5}}-5x^{-\frac{1}{5}} = \frac{x^{\frac{1}{5}}}{x^{1/5}}\left( x^{\frac{9}{5}}-4x^{\frac{4}{5}}-5x^{-\frac{1}{5}}\right) =x^{-\frac{1}{5}}(x^2-4x-5)
    Last edited by mr fantastic; January 29th 2011 at 01:56 PM.
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  4. #4
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    In fact, even ignoring the "absolute value" question "-6< x< 8" does NOT "describe the numbers that are between -6 and 8 inclusively. Because it does not include -6 and 8.
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