1. Chapter 1: Equations and Inequalities
Lesson 5: Solving Inequalities

2. Get Ready Open books to pg. 33 and read section “get ready”
If Kuni knows that she will use no more than 400 minutes per month, which plan is the best for her?
Ans plsn 1`

3. Key Terms
Trichotomy (tri-kot-uh-mee) Property: For any two real numbers, a and b, exactly one of the following statements is true.
a < b a = b a > b
Adding the same number to, or subtracting the same number from each side of an inequality does not change the truth of the inequality.

4. Key Concepts Name of Property Words Example
Addition Property of Inequality
For any real #, a, b & c
If a > b then
a + c > b + c
If a < b then
a + c < b + c
3<5
Then
3 + (-4) < 5 + (-1)
-1 < 1

5. Key Concept Name of Property Words Example
Subtraction Property of Inequality
For any real #, a, b & c
If a > b then
a - c > b - c
If a < b then
a - c < b - c
3<5
Then
3 + (-4) < 5 + (-1)
-1 < 1

6. Example 1:
Solve 7x-5>6x+4 graph the solution set on the number line
7x-5>6x+4
7x – x > 6x x Add -6x to both sides
x -5 > 4 simplify
X > add 5 to both sides
x > 9 simplify
What will the graph look like?

7. Key Concept Name of the property Words Example
Multiplication property of Inequality
For any real number: a, b, & c
c is positive
If a > b  ac > bc
If a < b  ac < bc
c is negative
If a > b  ac<bc
If a < b  ac>bc
-2< 3
-2(4)< 3(4)
-8< 12
5 > -1
5(-3)<-1(-3)
-15 < 4

8. Key Concept Name of the property Words Example
Division Property of Inequality
For any real number: a, b, & c
c is positive
If a > b  a/c > b/c
If a < b  a/c < b/c
c is negative
If a > b  a/c<b/c
If a < b  a/c>b/c
-18< -9
-18/3< -9/3
-6 < -3
12 > 8
12/-2<8/-2
-6 < -4

9. Key Term
Set builder notation: this is a way that the solution set of an inequality can be expressed.
Set builder notation = {x I x > 9}
This is read “the set of all numbers such that x is greater than 9.
See examples

10. Homework: pg 37-38, #11-43 odd
Classwork: pg #1-9