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## Main Question or Discussion Point

prove the folowing and state when the inequality holds...

|x+y+z|<=|x|+|y|+|z|

i was thinking that i consider all the possible cases, ie x is positive, y positive, z positive; then the various combinations with negative as well.....

is there another shorter method of doing it?

help.....

|x+y+z|<=|x|+|y|+|z|

i was thinking that i consider all the possible cases, ie x is positive, y positive, z positive; then the various combinations with negative as well.....

is there another shorter method of doing it?

help.....