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# Week 3 in Pre-Calc 11

Something I’ve learned this week is about absolute values.

Absolute value doesn’t really have a definition. Technically, absolute value is how far away a number from zero is.

The symbol for absolute value is: ∣

And the value should be inside of those straight lines. E.g. x

So, this is how it works. First, let’s look at this number line… As we can see, “3” is 3 lines away from zero and “-3” is also 3 lines away from zero.

So| 3 | (read as: the absolute value of 3) is 3 and | -3 | is also 3.

Why? Because recalling the technical definition of absolute value, it says “how far” a number is from zero and it’s not asking in which direction it’s from zero. In other words, the absolute value of a number is always positive!

The technical definition should also be like this: Meaning, the square root and the power of 2 (or square) will cancel each other out.

NOTE: Absolute value doesn’t work like parentheses. | | should not be mistaken as ( ).

For example, -(-2) is NOT -|-2| because:

-(-2) = +2

-|-2| = -(2) = -2