Absolute Values

Summary

• The absolute value of \(x\) , denoted by \(\left| x \right|\) is defined as

\[\left| x \right|=\{ \right.\]

• \(\left| x \right|≥0\) for all real numbers \(x\)
• \(\left| x \right|<a\) is the same as \(-a<x<a\)
• \(\left| x \right|≤a\) is the same as \(-a≤x≤a\)
• Note,

\[\sqrt{x^2}=\left| x \right|\]