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Math Help - Inequality and Interval Notation?

  1. #1
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    Inequality and Interval Notation?

    I have to solve the following inequality, answer written in interval notation

    x/(x+3)<_ (-8)/(7(x-6))
    BTW <_ is supposed to mean less than or equal to, I was unsure how to insert that.
    I get this answer every time, which apparently is wrong:
    7x^2-42x<_-8x -24
    7x^2-34x+24<_0
    (7x-6)(x-4)<_0
    [6/7,4]
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  2. #2
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    Quote Originally Posted by katekate View Post
    I have to solve the following inequality, answer written in interval notation
    x/(x+3)<_ (-8)/(7(x-6))
    This is an equivalent problem.
    \frac{{(7x - 6)(x - 4)}}{{7(x + 3)(x - 6)}} \leqslant 0.
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  3. #3
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    I don't mean to sound dense but that really did not help me, I don't understand what you mean.
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  4. #4
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    Quote Originally Posted by katekate View Post
    I don't mean to sound dense but that really did not help me, I don't understand what you mean.
    \frac{x}<br />
{{x + 3}} \leqslant  - \frac{8}<br />
{{7(x -6)}}\, \Rightarrow \,\frac{x}<br />
{{x + 3}} + \frac{8}<br />
{{7(x -6)}} \leqslant 0\, \Rightarrow \,\frac{{(7x - 6)(x - 4)}}<br />
{{7(x + 3)(x -6)}} \leqslant 0
    Last edited by Plato; September 17th 2009 at 10:39 AM.
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  5. #5
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    The equation was 7(x-6) in the second denominator, not +...not sure if this makes a huge difference but either way i don't understand how you went from the second step to the third.
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  6. #6
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    I corrected the typo.
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  7. #7
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    Okay, I've got it now. Thank you very much!
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