Algebra (Period 4)

Unions, Sets & Intersections 9-1

Conjunctions & Disjunctions 9-2

Conjunction = and --> the graph is an intersection ("yo") and inequality looks like our domains and ranges on our projects
EXAMPLE: 5 < x < 10 
open dots; between 5 and 10 is colored in 

Disjunction = or --> graph will go opposite ways ("dorky" dancer) and inequality looks like this:

x < -2 OR x > 4

open dots; one arrow goes right at 4 and the other arrow goes left at -2

Equations and Absolute Value 
1 VARIABLE
 9-3
Solve the equation twice - Once with the solution positive and once with it negative

I2x - 4I = 10

Solve it twice:

2x - 4 = 10 or 2x - 4 = -10

x = 7 or x = -3


If there is a term on the same side of the equation as the absolute value, move that to the other side of the equation first 
(just like we did with radical equations!) 
Then solve twice.


REMEMBER THAT THE SOLUTION GIVEN CANNOT BE NEGATIVE (the null set)




Inequalities and Absolute Value 
1 VARIABLE
 9-4
There are 2 possible types of inequalities - less than and greater than

For less thAND:

These are conjunctions and so you solve it twice and the solution ends up between them

I3xI < 15 is equal to -15<3x<15 
so x is greater than -5 and less than 5 
For greatOR than:

These are disjunctions and are solved twice with the solution infinitely in different directions

I3xI >15 is equal to 3x < -15 and 3x > 15