Algebra 2 Traditional9-14-2012

Representing the solutions of equalitiesYou can think of the solution(s) to a

given equation as solution sets.Equation Set notation Interval

notation3x+1 = 10

2x + 1 = 2x + 1

3x+4 = 3x – 7

Representing the solutions of equalitiesYou can think of the solution(s) to a given

equation as solution sets.Equation Set notation Interval

notation3x+1 = 10 {3} [3]

2x + 1 = 2x + 1 {x| x is a real number}

3x+4 = 3x – 7 { } ( )

( ,

Representing the solutions of in-equalities-2x + 4 > 8-2x > 4X < -2

{x| x<-2} (set builder notation)(-∞, -2) (interval notation)Number line (Draw below)

Quick final note…If an inequality includes an “or

equal to” part, that part remains even if you need to flip the inequality.

3 27

9

x

x

Before the next section: Operations with SetsGoals:

◦Know what it means to find the “intersection” and “union” between multiple sets.

◦Be able to graph unions and intersections on number lines

◦Define what an empty set, or “null” set is

Union & IntersectionsUnion: the set of elements in one set,

another, or both means the union of sets

“A” and “B”

Intersection: The set of elements that are in two sets at the same time

means the intersection of sets “F” and “G”

A B

F G

Pictorial Representations

Null or Empty SetsSets with no

elements in them are called null or empty sets.

{ } OR

Union and Intersection on the number lineUnion

x<4 OR x>0

Intersection

x<4 AND x>0

Absolute Value InequalitiesEverything you EVER wanted to know

about |2x-3|=, <, or > 9!

Type of Absolute Value

Problem|ax+b|

What it means in terms of distance

What kind of solution you are going to

get

|ax+b|=k

A specific distance “k” (to the left or right) away from zero on number line

|ax+b|>k

Two inequalities that won’t

overlap (so link them with a “U”)

|ax+b|<k

ax+b is BETWEEN “k” distance from zero to the left

and “k” distance to the right

Type of Absolute Value

Problem|ax+b|

What it means in terms of distance

What kind of solution you are going to

get

|ax+b|=k

A specific distance “k” (to the left or right) away from zero on number line

Two specific solutions

(assuming k>0)

|ax+b|>k

ax+b must be AT LEAST “k”

distance away from zero on number line

Two inequalities that won’t

overlap (so link them with a “U”)

|ax+b|<k

ax+b is BETWEEN “k” distance from zero to the left

and “k” distance to the right

Two inequalities that intersect, so

find the intersection

interval

Group Work/HWGroup Work:1.7 1-14

Homework1.715-43 oddTest early next week on chapter

1!