1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Absolute Value Equality

  1. Oct 19, 2013 #1
    1. The problem statement, all variables and given/known data
    abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement

    2. Relevant equations

    Triangle inequality?

    3. The attempt at a solution
    I have nothing :/
  2. jcsd
  3. Oct 19, 2013 #2


    User Avatar
    Science Advisor
    Gold Member

    What is the absolute value of x? if x => 0 then abs(x)=x, else it is -x.

    So make a table with all of the possible cases and see what happens!
  4. Oct 19, 2013 #3
    Drat, I was hoping that that I wouldn't have to do a case analysis; is there a more elegant way of solving this though?
  5. Oct 19, 2013 #4


    User Avatar
    Science Advisor
    Gold Member

    I don't know elegant ... I grew up on a farm!

    So once you have carried out the detailed work you can apply your own standards of elegance and cleverness ... and write something elegant!
  6. Oct 19, 2013 #5


    User Avatar
    Homework Helper

    Assume (by renaming of variables) that x ≤ y ≤ z. Then you have 4 cases to check, it shouldn't be too tedious.
  7. Oct 19, 2013 #6
    x + y + z <= |x| + |y| + |z|
    - x - y - z <= |x| + |y| + |z|

    (definition of the absolute value)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted