The formal definition of absolute value goes something like the following : "the magnitude of a real number without regard to its sign.".

#### What the heck does that mean ?

In plain "English", this means "how far from Zero" a number is, and the simplest way to understand this concept is by looking at some graphs!

Diagram 1 above shows the $$ |2| $$ on a number line. As you can see, both $$-2$$ and $$2$$ satisfy the $$ |2| $$ because both of those numbers are '2' units from zero!

Diagram 1 above shows the $$ |2| $$ on a number line. As you can see, both $$-2$$ and $$2$$ satisfy the $$ |2| $$ because both of those numbers are '2' units from zero!

### Example 2

Diagram 2 above shows the $$ |4| $$ on a number line. As you can see, both $$-4$$ and $$4$$ satisfy the $$ |4| $$ because both of those numbers are '4' units from zero!

### General Formula and Graph

'3' because $$ -3$$ and $$ 3 $$ are both the same distance from zero.

** no number** that satisfies this . Because $$ 5 \ne 4 $$ . And the distance form zero must be the same.