Inequalities With Linear Systems

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

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

Number Lines

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

Graphing

Point of Intersection

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

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

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

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?

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?

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

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