Absolute Values: Is it a Mistake or Something I Don't Know?

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Homework Help Overview

The discussion revolves around the properties of absolute values, particularly focusing on the transformation of expressions involving absolute values, such as \(\vert 5-x \vert\) and \(\vert x-5 \vert\). Participants are examining whether the textbook's example is correct or if there is a misunderstanding regarding absolute value properties.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the equivalence of \(\vert 5-x \vert\) and \(\vert x-5 \vert\) and question the reasoning behind this transformation. There are also inquiries about the implications of absolute values in different contexts, such as programming.

Discussion Status

Some participants have provided definitions and properties of absolute values, suggesting that \(\vert a \vert = \vert -a \vert\) is a key point in understanding the discussion. Multiple interpretations of the properties of absolute values are being explored, but there is no explicit consensus on the original question regarding the textbook example.

Contextual Notes

Participants are navigating through definitions and properties of absolute values, with some expressing uncertainty about the correctness of the textbook example. The discussion is framed within the context of homework help, indicating a learning environment where assumptions and definitions are being scrutinized.

Jeff Ford
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An example in my textbook gives

[tex]\vert \frac{5-x}{5x} \vert \Leftrightarrow \frac {1}{5} (\frac{1}{\vert x \vert}) (\vert x-5 \vert)[/tex]

Is there something I don't know about absolute values that allows [itex]\vert 5-x \vert[/itex] to become [itex]\vert x-5 \vert[/itex] or is this a mistake in the text?
 
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What would you say about |x| - |-x|?
 
It would be zero. So [tex]\vert 5 \vert + \vert -x \vert \Longleftrightarrow \vert -5 \vert + \vert x \vert[/tex]

Thanks for the push.
 
Well yes, but in your case |5-x| doesn't necessarily equal |5| + |-x|, but it does equal |x-5|, as you asked in the first place.
 
By definition |a|=|-a|. Let a=x-5 and the result is obvious.
 
TD said:
What would you say about |x| - |-x|?

[tex]\vert x \vert - \vert-x \vert = 0[/tex]

The absolute value a number simply means that its positive, no matter what. So abs(x) - (abs(-x) would be the same as abs(x) - abs(x). This is actaully quite usfull in the field of programming.
 
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