- #1

- 7

- 0

## 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|