Absolute value (other)

Absolute value can be applied to expressions, not just single numbers. For example, $|x - a|$ measures the distance between $x$ and $a$ on the number line. Absolute value is also used in inequalities, such as $|x - 3| < 2$, which describes all $x$ within 2 units of 3.

Important properties

• $|a - b| = |b - a|$ (distance is always non-negative and order doesn't matter)

• $|x - a| < r$ means $a - r < x < a + r$

• $|x - a| > r$ means $x < a - r$ or $x > a + r$