# Absolute Value Definition

In mathematics, the absolute value, also known as the modulus of real number, is defined as the non-negative number without any sign (-) used. It is written in the form of | x |. This absolute value is applied to form the zero origins to a digit of the coordinate system. We can use the absolute value on both scalars and vector quantities. A set of upward lines is used to represent absolute value, as shown in brackets (| |). For instance, the absolute value for 3 and -3 is the same |3|. For a more precise understanding, see the below diagram:

## Formula of Absolute Value

For a more precise understanding, let's assume x is a real number. Then the absolute value of x is determined as:

$\left| x \right| = \left\{ {\begin{array}{*{20}{c}} {x|if|x \ge 0}\\ { - x|if|x < 0} \end{array}} \right.$

That is,

|x| = x for a positive x
|x| = −x for a negative x (in 2nd case −x is positive), and |0| = 0.

Note:

To calculate the absolute value, you can use our Absolute Value Calculator.

### Example

For a better understanding, let's have an example below:

Suppose we have an equation having absolute value, for these, let's find the value of x (real number)

Given data

Equation : |5 - 2x| - 11 = 0

To Find

Absolute Value = ?

Solution

Let's solve this equation

|5 - 2x| = -11

Now expanding the absolute value as per the above-given formula:

5 - 2x = 11 , 5 - 2x = -11
-2x = 6 , -2x = -16
x = -3 , x = 8

Let's have a simple here, Find the absolute value for -|2| and |-2|.

As we know:

|x| = −x for a negative x (in which case −x is positive)

And,

|0| = 0.

So,

-|2| = -2 and |-2| = 2