MOD x explination please

w0lfed

I am having some troubles with the beggining 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)