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Solving inequalties

  1. Aug 5, 2005 #1
    Im trying to solve (4x-4)/(x+2)< 2x-3

    I get it down to 0<(2x+1)(x-2) if x+2>0

    0>(2x+1)(x-2) if x+2<0

    Are these right so far? Im not sure what to do now with the product being bigger or smaller than 0. Thanks for your time.
  2. jcsd
  3. Aug 5, 2005 #2


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    Right so far.
    You have products
    the sign of a product depends on the sighns of the factors
    a>0 and b>0
    a>0 and b<0
    a>0 and b<0
    a<0 and b>0

    another way to think about it is (2x+1)(x-2) is a continuos function
    find out where the zeros are
    call them a and b with a<b
    consider the intervals (since -2 is also an important number)
    all the points in one of these intervals satisfy the inequality or none do
    so checking one point in each intervals tells you if the whole interval satifies the inequality
    Last edited: Aug 5, 2005
  4. Aug 5, 2005 #3
    thanks lurf lurf .I got x>2. Does anyone know if that's right?
  5. Aug 5, 2005 #4


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    you missed -2<x<-1/2
    consider for example x=-1
    (4x-4)/(x+2)< 2x-3
    (4(-1)-4)/((-1)+2)< 2(-1)-3
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