What does |x| mean, and how can it be rewritten? When do you use it?
Thank you!

Question

What does |x| mean, and how can it be rewritten? When do you use it?
Thank you!

fibonaccichick666 · Answer

Can you tell me in what context it is used? or what level class you are in?

fibonaccichick666 · Answer

(As it can mean a few different things)

anonymous · Answer

For example: |(x^2)-2|x||=1
Soon university :)

anonymous · Answer

It means absolute value.
That means its value no matter what sign is in front of the number.

anonymous · Answer

Like |-6| would still be 6.

anonymous · Answer

So in this case: -2|x| would be 2x?

anonymous · Answer

Or if x would be -1, it would be 1?

fibonaccichick666 · Answer

not quite, because the -2 is not inside the absolute value, the condition of making it positive, does not occur

anonymous · Answer

No because -2 isn't in the absolute value brackets. BUT if it was |-2x| it would be 2x.

fibonaccichick666 · Answer

another way to represent absolute value is $abs(x)$  the graph looks like this:|dw:1399412353805:dw|

anonymous · Answer

Oh yes, now I remember! :) but how would I solve f ex: |(x^2)-2|x||=1

fibonaccichick666 · Answer

basically, all you do is make whatever is inside positive, so if you have, $|x-8|$, for x>8 you would have whatever x-8 is, but for x<8, you would have 8-x

fibonaccichick666 · Answer

so, now, for yours the first thing you want to think about is if that -2|x| is important.  Ie is there a difference between -2|-x| and -2|x|

anonymous · Answer

There wouldn't be a difference I'd say. But does it mean that x in |x-8| has to be more than 8? Or else |8-x|?

fibonaccichick666 · Answer

Correct, there is no difference.  
and let me elaborate for that example I gave you |x-8|   if you have x=9 it's |9-8|=|1|=1
but if you have x=7 it's |7-8|=|-1|=1=8-7    Do you see what I mean?

anonymous · Answer

Ooooh, now I get it!!! Yes, great explanation! Thank you so much!!!

fibonaccichick666 · Answer

np, so if you simplify the -2|x| part, you know that no matter what that is always going to be a minus sign in front of the two, do you see why?

anonymous · Answer

Yes, because its not inside the brackets :)

fibonaccichick666 · Answer

good so now let's say y=|2x| ok? (do you get why I can put the abs val around the two and keep the minus in front of the y? ) so you now have |x^2-y|=1

fibonaccichick666 · Answer

can you tell me two ways to write $|x^2-y|=1$ depending on your y value?

fibonaccichick666 · Answer

(just like |x-8| could be written as x-8 for x>8 and 8-x for x<8)