Home/Algebra/Numbers and algebraic properties/Absolute value1. Numbers and algebraic propertiesAbsolute valueLevel: fundamentalIn 1. Numbers and algebraic propertiesFormulaCopy LaTeX∣x∣={x,x≥0−x,x<0|x|=\begin{cases}x,&x\ge0\\-x,&x<0\end{cases}∣x∣={x,−x,x≥0x<0Tagsalgebraalgebra formulafundamentalsnumbers propertiesDetailRepresents the distance from a number to zero.Explore the ideaFound an error? Contact us.Related formulasRelatedDistance on the real lined(a,b)=∣a−b∣d(a,b)=|a-b|d(a,b)=∣a−b∣Open formulaOpen in sectionRelatedAbsolute-value equation∣f(x)∣=a ⟺ f(x)=a or f(x)=−a (a≥0)|f(x)|=a\iff f(x)=a\;\text{or}\;f(x)=-a\;(a\ge0)∣f(x)∣=a⟺f(x)=aorf(x)=−a(a≥0)Open formulaOpen in sectionRelatedAbsolute value and intervals∣x∣<a ⟺ −a<x<a;∣x∣>a ⟺ x<−a or x>a|x|<a\iff-a<x<a;\quad |x|>a\iff x<-a\;\text{or}\;x>a∣x∣<a⟺−a<x<a;∣x∣>a⟺x<−aorx>aOpen formulaOpen in section