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Homework Help: Solve inequality by factoring help

  1. May 14, 2008 #1
    x^2 + 8x + 15 > 0 solve inequality

    (X+5)(X+3)>0


    x+5>0 x>-5
    X+3>0 x>-3

    Why is the equality for X+5>0 x<-5 ? as the answers give?
     
  2. jcsd
  3. May 14, 2008 #2
    Because you have two possible solutions for (x+5)(x+3)>0

    the first one:

    x+5>0 ; x>-5

    x+3>0 ; x>-3

    [tex](-5, +\propto) \cap (-3, +\propto) = (-3, +\propto)[/tex]

    and the second

    x+5<0 ; x<-5

    x+3<0 ; x<-3

    [tex](-\propto, -5) \cap (-\propto, -3) = (-\propto, -5) [/tex]

    The final solution:

    [tex](-\propto, -5) \cup (-3, +\propto)[/tex]

    Anyway, this way is much more time-consuming... So you shouldn't use it in future.. There is much easier way...
     
  4. May 14, 2008 #3
    you could have just said

    "because if X > -5 then the first bracket will become negative and then (x+5)(x+3) wouldnt be > 0."


    but ok. =P

    btw : i just realised why
     
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