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: |a^{n}| = |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)