Pre Algebra (Period 2 & 4)

Absolute Value 1-4
ABSOLUTE VALUE IS ALWAYS POSITIVE!
(except zero because zero has no sign)
Absolute value is a DISTANCE concept and that is why it can't be negative.



I2000I read as the absolute value of 2000 and it equals 2000
I-2000I read as the absolute value of -2000 and it equals 2000

But look at -I1000I that's read as " the opposite of the absolute value of 1000 and so you take the absolute value of 1000, which is 1000 and then take the opposite. So it's value is -1000

This is even more challenging...
-I-300I that is the opposite of the absolute value of negative 300. So first, what is the absolute value of -300? Well, it has to be positive so its 300. but then you need to take the opposite of that so the answer is -300.

Always take the absolute value first. Then do the sign on the outside of the absolute value symbols.

What can the solution for InI = 5 be? That is, for what values of n is the absolute value = 5? Well, n can be -5 or 5. You write this in "set notation" {-5, 5}
because
the absolute value of -5 or I-5I = 5
and
the absolute value of 5 or I5I = 5

There are TWO answers for the absolute value of a variable ( except 0).
Zero is neither + or -. IT is neutral.


On the other hand, every integer has an ADDITIVE INVERSE which will be its OPPOSITE SIGN (except zero which has no sign - neutral)
5 + -5 = 0
-10 + 10 = 0

any integer + its additive inverse = 0
An integer can be -, +, or 0

All negative integers are less than zero.

The opposite of a positive number is a negative.

The absolute value of an integers is NEVER negative