# Thread: how to prove abs(a-b) <= abs(a) + abs(b)?

1. ## how to prove abs(a-b) <= abs(a) + abs(b)?

Hi guys, Im taking calculus in university but i'm having some trouble with some kinds of problems.

can some one help me prove this:

abs(a-b) <= abs(a) + abs(b) for all real numbers of a and b

i get very confused when i see abs values =((

2. The standard triangle inequality states that $|x+y|\le |x|+|y|$.

So let $x=a~\&~y=-b$.

3. Originally Posted by Plato
The standard triangle inequality states that $|x+y|\le |x|+|y|$.

So let $x=a~\&~y=-b$.
so do i sub a and -b into the standard triangle inequality equation?? and solve??

4. i really dont know how to start =(

5. Originally Posted by sam0812
i really dont know how to start =(
You have been told exactly what to do. What don't you understand about reply #2?

By the way: http://math.ucsd.edu/~wgarner/math4c...gleinequal.htm

6. Try assigning actual values to the variables and see if that makes more sense. Try using some easy numbers.

Maybe let a=2 and b=7.

Plug that into your original equation and see what happens.