Let's first discuss the term *absolute value*. The absolute value is fundamentally about **the distance between two values**, depending on the expression contained within the absolute value sign. For example, the distance between two numbers x and y can be written as |x – y|. Therefore:

**|x|**=**|x – 0|**is the distance of x from 0, the origin.**|x – 5|**is in fact the distance of (x – 5) from the origin. So another way of interpreting this is that**|x – 5| is the distance between x and 5**

Let's look at some more examples:

- |3 – 5| = |-2| = 2. In other words, 3 and 5 are a distance of 2 units apart.
- |-2 – 6| = |-8| = 8. In other words, -2 and 6 are a distance of 8 units apart.
- |4 – (-7)| = |4 + 7| = |11|. In other words, 4 and -7 are a distance of 11 units apart.

To summarize, **the distance between two numbers x and y is defined by a subtractive relationship: |x – y|**. Thus, when our 'y' term is positive (like 5), the distance between x and 5 is simply |x – 5|. When our 'y' term is negative (like -5), the subtraction sign gets converted to a plus sign, and the distance between x and -5 can be written as: |x – (-5)| = |x + 5|.

For further reading on absolute values, consider the following:

## Comments