Home/Algebra/Inequalities/Absolute value and intervals8. InequalitiesAbsolute value and intervalsLevel: fundamentalIn 8. InequalitiesFormulaCopy LaTeX∣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>aTagsalgebraalgebra formulainequalitiesDetailInterprets absolute-value inequalities as distances.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 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 section