Algebra Period 3

Compound Sentences 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 in this setting [ ] represents absolute value.
[2x - 4] = 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 us between them
[3x] < 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
[3x] >15 is equal to 3x < -15 and 3x > 15

INEQUALITIES IN 2 VARIABLES 9-5
You will shade an x y graph to find the side of a linear equation that fits the solution
EXAMPLE: x + y > 5
You graph the line with DOTTED line because it cannot be equal to 5
You pick an easy point on one side of the line and substitute to see if that side is a solution.
If that does not work, pick an easy point on the other side to see if that side checks.
I USUALLY USE (0,0) as my first point!
If there is more than 1 Inequality (a system of inequalities), follow the same procedure and where the 2 shadings overlap each other is called the solution of the system of inequalities.

SYSTEMS OF INEQUALITIES IN TWO VARIABLES 9-6
If there is more than 1 Inequality (a system of inequalities),
1. Follow the same procedure as above for one equation
but you will need to do it for each equation.
2. Use a different type of shading for each so you won't get confused
(Ex: Use slanted lines one way and then slanted lines the other way. Use different colors if possible. Make one set of lines wavy and the other set straight)
3. Where the 2 shadings overlap each other is called the solution of the system of inequalities.
(any point in the overlap should work in BOTH inequalities - make sure you check!!!!!)