Advanced Math / Absolute Value Inequalities
Absolute value inequalities
Absolute value inequalities describe distances. Less-than inequalities produce inside intervals; greater-than inequalities produce outside intervals.
Least you need to know
- $|x-a|<r$ means $a-r<x<a+r$.
- $|x-a|>r$ means $x<a-r$ or $x>a+r$.
- Endpoint inclusion follows the original inequality symbol.
Key notation
- r — A positive radius or distance from a center
Worked example
For $|x-4|\le 6$, the values of $x$ are within 6 of 4, so $-2\le x\le 10$.
Common mistakes
- Less than uses and; greater than uses or.
- Strict endpoints are not counted in integer counts.
How to recognize it
- The problem asks for an interval or number of integer values.
- The stem uses words like within, farther than, at most, or more than.
Pelajaran seterusnya yang disyorkan
Lanjutkan topik ini dengan Equivalent Exponential Expressions.
Equivalent Exponential ExpressionsPelajaran berkaitan
Lanjutkan dengan pelajaran terdekat dalam topik yang sama.