1. Inequalities
Absolute Value

2. 1 block
1 block
You walk directly east from your house one block. How far from your house are you?
You walk directly west from your house one block. How far from your house are you?
It didn't matter which direction you walked, you were still 1 block from your house.
This is like absolute value. It is the distance from zero. It doesn't matter whether we are in the positive direction or the negative direction, we just care about how far away we are.
4 units away from 0
4 units away from 0 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8

3. Everything in between these lines is less than 3 units away from 0
Let's look at absolute value with an inequality.
This is asking, "For what numbers are the distance from 0 less than 3 units?" 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8
Everything in between these lines is less than 3 units away from 0
X < 3
X > - 3
AND
Inequality notation
Interval notation
This means x is greater than -3 AND x is less than 3 (or x is inbetween -3 and 3)

4. OR What if the inequality is greater than? In interval notation:
This is asking, "When is our distance from 0 more than 5 units away?" 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8
Everything outside these lines is more than 5 units away from 0
Everything outside these lines is more than 5 units away from 0
We'll have to express this with two difference pieces OR
In interval notation: