SOLUTION: College algebra help? Show that {{{ a <= abs(a) }}}? I thought that maybe I could show that {{{ a - abs(a) <= 0 }}} but I don't even know how to start. Thanks in advance if you

Algebra ->  Absolute-value -> SOLUTION: College algebra help? Show that {{{ a <= abs(a) }}}? I thought that maybe I could show that {{{ a - abs(a) <= 0 }}} but I don't even know how to start. Thanks in advance if you       Log On


   



Question 660689: College algebra help? Show that +a+%3C=+abs%28a%29+?
I thought that maybe I could show that +a+-+abs%28a%29+%3C=+0+ but I don't even know how to start. Thanks in advance if you can help :-)

Found 2 solutions by jim_thompson5910, math-vortex:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28a%29+=+a if a%3E=0

So if a%3E=0, then

+a+%3C=+abs%28a%29+

becomes

+a+%3C=+a+

which is certainly true.

-------------------------------------------------------

abs%28a%29+=+-a if a%3C0

So if a%3C0, then

+a+%3C=+abs%28a%29+

becomes

+a+%3C=+-a+

which is also true (since 'a' is negative, '-a' is positive)
==================================================================

These two cases exhaust all possibilities

So this proves that +a+%3C=+abs%28a%29+ is always true for any value of 'a'.

--------------------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
--------------------------------------------------------------------------------------------------------------

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

You could start by dividing your proof into three cases:
a is negative (i.e. a<0).
a is positive (i.e a>0).
a is zero (i.e. a=0). This is the easy one (o:

Show what the absolute value function does to a in each case. Start there and see how far you 
get. You may email me directly if you have more questions, or repost here.

Then again, another tutor might post the whole proof for you (o:

Mrs. Figgy
math.in.the.vortex@gmail.com