Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    lurflurf

    User Avatar
    Homework Helper

    Right so far.
    You have products
    the sign of a product depends on the sighns of the factors
    ab>0
    means
    a>0 and b>0
    or
    a>0 and b<0
    ab<0
    means
    a>0 and b<0
    or
    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)
    x<-2
    -2<x<a
    a<x<b
    b<x
    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

    lurflurf

    User Avatar
    Homework Helper

    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
    (-4-4)/1<-2-3
    -8<-5
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solving inequalties
  1. Solve For It (Replies: 2)

  2. Solve It! (Replies: 2)

  3. Solve The Series (Replies: 2)

Loading...