1. Inequalities With Linear Systems

2. Vocabulary Linear Combination Method Symbol Inequality Solution
Geometry
Variable
Equation
Algebra
Greater Than
Fraction
Problem Solving Strategies
Less Than
Decimal
Equal To
Point of Intersection
Midpoint
Substitution Method
Linear System
Number Line

3. Symbols
Greater Than > Less Than < Equal To = Greater Than or Equal To > Less Than or Equal To <

4. Number Lines

5. Using a Number Line What numbers satisfy this equation?
3X + 4 < 13
What numbers satisfy this equation?
-What numbers satisfy this equation?

6. Graphing

7. Point of Intersection

8. Problem Solving Strategies
Make A Table
Draw a Picture
Solve a Simpler Problem
Make an Equation K
Guess and Check

9. 6 Step Method Set Equations Equal Get All X’s on One Side
Get All Numbers on One Side
X = ?
Substitute X Back Into One Equation
Point of Intersection

10. Combination Method Get X and Y on the Same Side
Make Sum of 2 Equations = Sum of Totals
Solve for X
Plug X Back Into an Equation From Step One
Solve for Y

11. Problem 2.1
1. What kinds of equations will show how the costs for the two companies are a function of the number of days? 2. What pattern do you expect to see in graphs of the equations? 3. How can you use a graph to answer the questions about which company offers the best price?

13. 2.1 Continued
For what number of days will the costs for the two companies be the same? What is that cost?
For what numbers of days will Super Locks cost less than Fail Safe?
For what numbers of days will Super Locks cost less than $6000?
What is the cost of one year of service from Fail Safe?
How can Fail Safe adjust its per-day charge to make its cost for 500 days of service cheaper than Super Locks’ cost?

14. 2.1 Continued
B. For each company, write an equation for the cost c for days d of security services.

15. Problem 2.2 C = 3,975 + 6d (Super Locks) C= 995 + 17.95d (Fail Safe)
Find Point of Intersection:
Using 6 Step Substitution Method
Using Combination Method