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Concept

Absolute Value

The absolute value of a number is the distance between and on the number line. It is denoted as and it is always a non-negative value.
Interactive number line illustrating the concept of absolute value
The absolute value is defined for any real number. The absolute value of a negative number is its opposite value, while the absolute value of a positive number is equal to itself.

Absolute Value Properties

There are several properties and identities that are useful when simplifying expressions or solving equations dealing with absolute values. For any two real numbers and the following relationships and identities hold true.

Property Algebraic Representation
Non-negativity
Symmetry
Idempotence
Positive-definiteness
Identity of Indiscernibles
Multiplicativity
Preservation of Division
Subadditivity
Triangle Inequality