# What does Absolute Value Equations mean?

**What does Absolute Value Equations mean?**

An absolute value equation in mathematics is an equation that contains an absolute value expression. x+1 x+1 the absolute value indicates how far the number is from zero. Negative values are not permitted. It refers to the size or magnitude of the number.

Absolute Value Sign

The absolute value of a number is determined by its distance from its origin on the number line. It also indicates the number's polarity, whether it is negative or positive. It can be negative, but it can also show the distance. It is always positive.

Absolute Values:

You can think of the absolute value as the distance between 0 and 0 on a number-line.

The absolute value of 5 is 5 written | 5 | = 5

**The value of -4 is 4 written | -4 | = 4**

The value of -8 is -8 written | -8 | = 8

How can you calculate absolute value?

The absolute value is the distance a number has from zero. This value will always be positive. If there is a negative sign, remove it to make the number absolute. So, for example, negative 4 could be 4.

Solved examples on Absolute Value

Example 1 Calculate the absolute value for 25 using the online absolute calculator.

Solution:

The formula is as follows:

|x|= x, if x > 0 (x is positive)

|25| = 25.

**Therefore, 25 is the absolute value.**

Example 2 Calculate the absolute value of -25.2 using the online absolute calculator.

Solution:

The formula is as follows

|x| = -x, if x < 0 (x is negative)

|-25.2| = - (-25.2) = 25.

Therefore, the absolute value for -25.2 is 25.2.

Use the online absolute value calculator to find the absolute values for the following numbers.

7.2

-5.6

This is manual method and formulas to calculate it by hand. It is very long procedure. Now some online tool such as provides you the results within a few seconds without any mistakes.

**How do I represent absolute values on a number line?**

It is not difficult to use a number line. The absolute value of the number lines is also represented when the results are displayed following processing with the absolute value calculator.

**Absolute value of a real number**

The following conditions will apply if x is a real number.

| x | = x, if x >= 0

| x | = - x, if x < 0

Let's examine the absolute value for 2 as shown in the following number line. 2 Also, +2 and 2 are the distances of 2 from the origin. It would still be 2 since distance is not measured in negative.

**Absolute value of complex number**

Complex numbers are made up of both real and imaginary numbers. It is therefore difficult to determine the absolute value of complex numbers, unlike integers. Let's say that x+iy represents the complex number.

z = x+iy

**The absolute value for z will be:**

|z|= [Re(z)2+Im(z)2]

|z| = (x2+y2)

Where x and y are the real numbers.

**Absolute Value in Number Line**

The absolute value graph is a graph that shows absolute values. We know that the absolute value for any real number is always positive so any function graph or number will have an absolute value only on the positive side.

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