Home/Algebra/Equations/Absolute-value equation7. EquationsAbsolute-value equationLevel: fundamentalIn 7. EquationsFormulaCopy LaTeX∣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)Tagsalgebraequationsalgebra formulaDetailTurns an absolute-value equation into two cases.Explore the ideaFound an error? Contact us.Related formulasRelatedAbsolute value∣x∣={x,x≥0−x,x<0|x|=\begin{cases}x,&x\ge0\\-x,&x<0\end{cases}∣x∣={x,−x,x≥0x<0Open 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