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)

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving