- #1
clarence829
- 7
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Homework Statement
Prove the following inequalities for all numbers x, y.
|x+y| ≥ |x|-|y|
[Hint: Write , and apply , together with the fact that
Homework Equations
These were given as hints in my textbook:
x=x+y-y
|a+b| ≤ |a| + |b|
|-y|=|y|
The Attempt at a Solution
I realize that this is very elementary but this is my first day teach myself calculus and that I am inexperienced using proofs in math. Any and all help is greatly appreciated.
1) x=x+y-y
2) |x+y|≤|x|+|y|
3) |-y|=|y|
4) x+y=x+y
5) √(x+y)^2=√(x+y)^2
6) |x+y|=|x+y|
7) |x+y|≤|x|+|y|
8) |x+y|≤|x|+|-y|