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EV33

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## Homework Statement

prove that llal-lbll[tex]\leq[/tex]la-bl

## Homework Equations

Triangle inequality

lx+yl[tex]\leq[/tex]lxl+lyl

## The Attempt at a Solution

Let a=(a-b)+b

By using the triangle inequality we get

lal-lbl[tex]\leq[/tex]la-bl

Then from here I am not sure what I can do. I would like to say on the left hand side that I can use the triangle inequality again by taking the absolute value of the left side and saying that I have the absolute value of a plus -absolute value of b.

llal+(-lbl)l[tex]\leq[/tex]lal-lbl[tex]\leq[/tex]la-bl

My second thought it instead of doing that I could possible just take the absolute value of both sides and then I would get what I was trying to prove because taking the absolute value of the right side wouldn't change anything, but taking the absolute value of the left side would change it exactly the way I need it to be.

I was wondering if either one of those Ideas is legitament because I am really not sure about them. If neither one is could someone point me in the right direction in proving this. Thank you for your time.

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