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!
picture of absoltue value of 2 on number line
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

picture of absoltue value of 4 on number line
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

general formula graph absolute value
Problem 1

What number can replace the question mark ? ( Can you figure out what absolute value that the number line graph below represents ?)

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

Problem 2

What number can replace the question mark ? ( Can you figure out what absolute value that the number line graph below represents ?)

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


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