# Absolute value proof

1. Nov 7, 2012

### Bipolarity

1. The problem statement, all variables and given/known data
If a,b,c and are all positive, and if $|a-b| < c-b$, then prove or find a counterexample to $|a|<c$

2. Relevant equations

3. The attempt at a solution
So far I have been able to show $|a-b|<c$ but don't know what to do next.

THanks!

BiP

2. Nov 7, 2012

### SammyS

Staff Emeritus
You proved that $|a-b|<c \ ?\ \$ How did you do that?

Let a = 1, b = 10 and c = 2 .

3. Nov 7, 2012

### Bipolarity

Hey Sammy, I think I edited the problem before your post, I don't know how this happened. Please read my edited post again thanks.

BiP

4. Nov 7, 2012

### skiller

I think you are a bit confused. For example, why do you have $|a|$ when you know that $a$ is positive anyway?

5. Nov 7, 2012

### micromass

Staff Emeritus
Use

$$a=(a-b)+b$$

6. Nov 7, 2012

### Bipolarity

I see! Do you want me to then use the fact that $|a+b| ≤ |a|+|b|$ Thanks micro!

BiP

7. Nov 7, 2012

### micromass

Staff Emeritus