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Absolute Value Equality

  • Thread starter lepton123
  • Start date
  • #1
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Homework Statement


abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement


Homework Equations



Triangle inequality?

The Attempt at a Solution


I have nothing :/
 

Answers and Replies

  • #2
UltrafastPED
Science Advisor
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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!
 
  • #3
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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?
 
  • #4
UltrafastPED
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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!
 
  • #5
verty
Homework Helper
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Assume (by renaming of variables) that x ≤ y ≤ z. Then you have 4 cases to check, it shouldn't be too tedious.
 
  • #6
x + y + z <= |x| + |y| + |z|
- x - y - z <= |x| + |y| + |z|

(definition of the absolute value)
 

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