simple inequalities (1 Viewer)

[enveloped]

hey,
just a simple question
1)whats the triangle rule? the thing abt adding the sides together? (sorry that wasnt inequalities)
2) when u do absolute values such as
|x|+x = 2x if x is greater or equal to 0 or
= 0 if x < or equal to 0
do u need the " or equal to" in the 2nd bit when uve already mentioned it in the first bit? coz i didn't bt then the answers did.
3) for |x|+|y| i did:

1. x+y if x,y is greater or equal to 0
2. y-x if x<0 and y is greater or equal to 0 or
3. -x-y if x<0 and y < 0
4. x-y if x is greater or equal to 0 and y <0

bt the answers only gave 1 and 4( with the 4th saying y is less or equal to 0...why?) so i was wondering why??
thanks in advance!
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[Trebla]

1) I think you mean the triangle inequality. The sum of any two sides is always greater than the third side. i.e. for triangle ABC: AB + BC > AC

2) For |x|+x = 2x
=> |x| = x
Since the left hand side is always positive or zero, therefore x (on the right hand side) is always a positive number or zero. By inspection it is obvious that negative numbers do not satisify the equation. Therefore, the answer is just x ≥ 0.
You do not need to mention a solution more than once.

3) Need more detail on what exactly you are trying to solve...

 

[enveloped]

thanks trebla for the 1st one
for 2: the answers said : |x|+x = 2x if x is greater or equal to 0 or
= 0 if x < or equal to 0
but i put |x|+x = 2x if x is greater or equal to 0 or
= 0 if x < 0
so i was wondering if u need the "or equal to"
for 3: the questions from fitzpatrik 2-u 3(d) q6 and it just says write expressions for the following
help?