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

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Homework Help Overview

The discussion revolves around the relationship between three positive variables a, b, and c, specifically examining the implications of the inequality |a-b| < c-b and whether it leads to the conclusion that |a| < c.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the implications of the given inequalities and are questioning the validity of the assumptions made, particularly regarding the positivity of a. There are also attempts to provide specific values for a, b, and c to explore the relationship further.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning each other's reasoning. Some guidance has been offered regarding the use of mathematical properties, but no consensus or resolution has been reached yet.

Contextual Notes

There is a noted confusion regarding the use of |a| given that a is stated to be positive. Additionally, the original poster has edited their problem statement, which may have contributed to the confusion among participants.

Bipolarity
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Homework Statement


If a,b,c and are all positive, and if |a-b| &lt; c-b, then prove or find a counterexample to |a|&lt;c

Homework Equations


The Attempt at a Solution


So far I have been able to show |a-b|&lt;c but don't know what to do next.

THanks!

BiP
 
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Bipolarity said:

Homework Statement


If a,b,c and are all positive, prove or find a counterexample to
|a-b| &lt; c-b

Homework Equations



The Attempt at a Solution


So far I have been able to show |a-b|&lt;c but don't know what to do next.

THanks!

BiP
You proved that |a-b|&lt;c \ ?\ \ How did you do that?

Let a = 1, b = 10 and c = 2 .
 
SammyS said:
You proved that |a-b|&lt;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
 
Bipolarity said:
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?
 
Use

a=(a-b)+b
 
micromass said:
Use

a=(a-b)+b

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

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

BiP

Don't ask, try! :biggrin:
 

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