Absolute Value Rules
Algebra rules for absolute values are listed below.
1. |–a| = |a|
2. |a| ≥ 0
3. Products: |ab| = |a||b|
4. Quotients: |a / b| = |a| / |b|
5. Powers: |an| = |a|n
6. Triangle Inequality: |a + b| ≤ |a| + |b|
7. Alternate Triangle Inequality: |a – b| ≥ |a| – |b|
Differences:
|a – b| is not the same as |a| – |b|
See also
Absolute value of a complex number, triangle inequality (geometric)