1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math proof homework problem

  1. Jan 24, 2008 #1
    How do I prove that: [​IMG]?
  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!
  4. Jan 24, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?