Meaning of Absolute value

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!

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.

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

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