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October 24th, 2016, 10:13 AM   #1
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Verify rule for absolute value

Hi guys, could someone help on how to tackle these two problems I am not quite how to tackle these.

I think the first one is a triangle inequality but not too sure? I really don’t know about the second.

Do I use the equation given and start from there or do I derive it some how from an absolute value.I can see if i plug number in it works but that it really.


Questions are below:

Q1. Verify the rule that for two real numbers x and y then

$\displaystyle |x+y| < |x|-|y|$ (suppose to be less than equal too)

Q2. Given that for two real numbers x and y, $\displaystyle |x+y|<|x|+|y|$, deduced that $\displaystyle |x-y|<|x|-|y|$ (once again suppose to be less than equal to.)
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October 24th, 2016, 01:42 PM   #2
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They are both wrong. Counterexamples: for Q1, let x=y, while for Q2 let x=-y.
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