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Homework Help: Math proof homework problem

  1. Jan 24, 2008 #1
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jan 24, 2008 #2
    well here it is what i would do, consider first the values of x,y<-1 and you will get
    I x-1 I= -(x-1) and I y+1 I= -(y+1), in which case you would get -3+2 which is smaller than 5.
    then -1<x,y<1, in which case you would get
    Ix-1I= -(x-1) and for Iy+1I= y+1, see what happens now when you plug in???
    and the other case would be x,y>1
    In which case you would ged
    Ix-1I=x-1 and Iy+1I=y+1 when you plug in see what u get.

    Note; this is not exactly as i am saying but i did it in purporse, this is the idea, but just that you have to do it in a better order, like taking the values of x smaller/greater than sth first, and then those of y, etc

    P.s.Show some work of yours first, and then maybe you will get some more help!
     
    Last edited by a moderator: May 3, 2017
  4. Jan 24, 2008 #3

    nicksauce

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    What is the maximum value of (x-1) / |x-1| ?
     
  5. Jan 25, 2008 #4
    Since the OP hasn't shown up yet, i will give him/her some more hints.
    Indeed, i will just pick up at what nicksauce suggested, it is shorter and nicer, look teh maximum value of [tex]\frac{(x-1)}{ abs{(x-1)}}[/tex], well the maximum here is 3.
    Now look at the other part what is the minimum value of
    [tex]2\frac{(y+1)}{abs(y+1)}[/tex], obviously it is -2, or you might want to look for the maximum of the:
    [tex]-2\frac{(y+1)}{abs(y+1)}[/tex], which would be 2,
    now going back to what you have to prove, why does that inequality hold?
    Can you figure it out now, do u understand how it goes?
     
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