Is |a|<c possible when |a-b|<c-b?

[Bipolarity]

Homework Statement

If a,b,c and are all positive, and if $|a-b| < c-b$, then prove or find a counterexample to $|a|<c$

Homework Equations

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

 

[SammyS]

Homework Statement

If a,b,c and are all positive, prove or find a counterexample to
$|a-b| < c-b$

Homework Equations

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

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

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

 

[Bipolarity]

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

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

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

 

[skiller]

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

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

 

[micromass]

Use

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

 

[Bipolarity]

Use

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

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

BiP

 

[micromass]

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

BiP

Don't ask, try!