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Math Help - inequality

  1. #1
    Junior Member
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    inequality

    Im not sure how to answer this question! Either I square both sides, change the inequality and get a very confusing polynomial degree 4 taking or I take away modulus sign giving me the fraction in the middle where I dont know what to do. Ive never been shown how o do this type of question so if someone could help me out that would be great. thnx
    solve \frac{2x+3}{x-5}<the modulus of  \mid \frac{4x+12}{x+1}\mid

    ps sorry I couldnt work out the modulus sign to cover two lines but the modulus is of the whole fraction on the RHS
    Last edited by oxrigby; November 5th 2008 at 01:55 PM.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    \frac{2x+3}{x-5}<\left| \frac{4x+12}{x+1} \right| implies that \frac{4x+12}{x+1}>\frac{2x+3}{x-5} or \frac{4x+12}{x+1}<-\frac{2x+3}{x-5}. Do each one of them. Solution set is the union of solution for the first inequality and the second one.
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  3. #3
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    thanks i got \frac{2\sqrt{17}}{4}<x<\frac{\sqrt{58}+1}{3} is this the right answer and what you mean by union? thanks
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