Triangle Inequality: Explained with Examples

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SUMMARY

The discussion centers on the Triangle Inequality theorem, specifically addressing the expression |(x-1)^2-5x+4| and its relation to |x-1|. A participant mistakenly equates the expression with -3(x-1), which is clarified as incorrect. The correct interpretation of the Triangle Inequality is established as |x±y| ≤ |x| + |y|, confirming the validity of the inequality while highlighting the error in the initial equality.

PREREQUISITES
  • Understanding of algebraic expressions and manipulations
  • Familiarity with the Triangle Inequality theorem
  • Basic knowledge of absolute values in mathematics
  • Ability to interpret and analyze mathematical inequalities
NEXT STEPS
  • Study the properties of absolute values in algebra
  • Explore advanced applications of the Triangle Inequality in real analysis
  • Learn about inequalities in mathematical proofs
  • Investigate common misconceptions related to algebraic identities
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Students of mathematics, educators teaching algebra and inequalities, and anyone interested in deepening their understanding of mathematical concepts related to the Triangle Inequality.

kingyof2thejring
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|(x-1)^2-5x+4|=|(x-1)^2 - 3(x-1)| <= |x-1|^2+3|x-1|
how does that work? i thought triangle inequaility was |x+y| <= |x|+|y|
please explain thanks in advance
 
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Well the first equality is false. - 3(x-1) \neq-5x+4. But the inequality is correct. The triangle inequaity says that

|x±y|\leq|x|+|y|
 

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