Understanding Modulus and Absolute Values: Explanation and Examples

[w0lfed]

I am having some troubles with the beginning ideas about modulus and absolute values etc...

i understand the basics about it but get a bit confused when they ask for the sum of different expressions or the product of different expressions
eg

|x - 1| + |x + 1| < 1

or

|x - 2|.|3x + 1| >2

if someone could explain this so its quite easy to understand and NOT just complete these examples but explain the concepts!

Much appreciated

 

[mathman]

The general idea is to break up the question into several questions without | |. For example - the first expression:
For x > 1, (x-1)+(x+1) > 1, which becomes 2x > 1, or x > 1/2 (all x in range)
For 1> x > -1, (1-x)+(x+1)>1, which becomes 2 >1. (all x in range)
For -1 > x, (1-x)-(1+x) > 1, which becomes -2x > 1, or x < -1/2 (all x in range)