Proving the Triangle Inequality for Real Numbers

[Fairy111]

Homework Statement

For real numbers x(1), x(2), ..., x(n), prove that |x(1) + x(2) +...+x(n)| <= |x(1)|+...|(n)|

Homework Equations

The Attempt at a Solution

Maybe begin with prooving that x <= |x| ? I am not sure how to do this though.
Any help or hints would be great, as I am really stuck on this.

 

[radou]

Homework Statement

For real numbers x(1), x(2), ..., x(n), prove that |x(1) + x(2) +...+x(n)| <= |x(1)|+...|(n)|

First of all, one can prove that, for some real numbers a, b, |a + b| <= |a| + |b|. Any ideas how to generalize? Try to use this inequality to show that |a + b + c| <= |a| + |b| + |c|, for some given real numbers, a, b and c.