The absolute value of a real number is written as |x| and is defined as:
The absolute value of x is always greater than or equal to zero. On the real number line, the absolute value of a number is equal to its distance from the origin.|x| = x if x ≥ 0 |x| = -x if x < 0
|<----|-4|----->|<-------|5|------->|
--+---+---+---+---+---+---+---+---+---+---+--
-4 -2 0 2 4
The absolute value of the difference between two real numbers is the distance between them on
the real number line.
|<-------------|-4 - 5|------------>|
--+---+---+---+---+---+---+---+---+---+---+--
-4 -2 0 2 4
The absolute value of an expression has the following properties
|a·b| = |a||b|
|an| = |a|n
|a/b| = |a|/|b| where b ≠ 0
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|a| = √ a2
|a + b| ≤ |a| + |b| triangle inequality
|a| ≤ k if and only if -k ≤ a and a ≤ k
|a| ≥ k if and only if -k ≥ a or a ≥ k
8.1. Solving equations with absolute values
8.2. Solving inequalities with absolute values
8.3. Absolute values of complex numbers
8.4. Solved problems