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Absolute Value Formula

Absolute value represents the distance of a number from zero on the number line, regardless of whether the number is positive or negative. It is written using vertical bars, such as |x|.

Absolute Value Formula

The absolute value of a number x is defined as:

|x| = x, if x ≥ 0

|x| = −x, if x < 0

This means a positive number stays positive, while a negative number becomes positive when its absolute value is taken.

Examples of Absolute Value

For a positive number:

|7| = 7

For a negative number:

|−7| = 7

For zero:

|0| = 0

Absolute Value in Equations

When solving an equation such as |x| = 5, there are two possible values of x because both 5 and −5 are 5 units from zero.

x = 5 or x = −5

Absolute Value as Distance

Absolute value can also be used to find the distance between two numbers. The distance between a and b is:

|a − b|

For example, the distance between 3 and −4 is:

|3 − (−4)| = |7| = 7