Chapter Inequalities and Absolute Value
An inequality asks not for the value that balances an equation but for the whole set of values that satisfy a condition, and that set is usually an interval or a union of intervals. The absolute value \(|a-b|\) measures the distance between \(a\) and \(b\text{,}\) so equations and inequalities involving absolute values are statements about distance. In calculus these skills are used constantly: finding where a function is defined, where it is positive, and where it is increasing all come down to solving an inequality, often by testing the sign of each factor on a number line (a sign chart).
Topics
-
Interval notation: converting between set-builder notation, number lines, and intervals
-
Absolute value equations, and absolute value as distance
-
Linear and compound inequalities
-
Absolute value inequalities
-
Polynomial and rational inequalities via sign charts
Resources
Section 2.7 of OpenStax College Algebra, and Paul’s Online Notes on polynomial and rational inequalities.
