6-5 linear inequalities. problem 1: identifying solutions of a linear inequality
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6-5 Linear Inequalities
Linear Inequality: in two variables, such as can be formed by replacing the equal sign in a linear equation with an inequality symbol
Solution of an inequality: in two variable is an ordered pair that makes the inequality true.
Problem 1: Identifying Solutions of a Linear Inequality
Is the ordered pair a solution of
(1,2)
Is (-3,-7) a solution of ?
The graph of a linear inequality in two variables consists of all points in the coordinate plane that represents solutions. The graph is a region called half-plane that is bounded by a line. All points on one side of the boundary line are solutions, while all points on the other side are not solutions
Problem 2: Graphing an Inequality in Two Variables
What is the graph of
What is the graph of
What is the graph of
What is the graph of
Problem 3: Graphing a Linear Inequality in One Variable
What is the graph of
What is the graph of
What is the graph of
What is the graph of
Problem 4: Rewriting to Graph an Inequality
An interior decorator is going to remodel a kitchen. The wall above the stove and the counter is going to be redone as shown. The owners can spend $420 or less. Write a linear inequality and graph the solutions. What are 3 possible prices for the wallpaper and tiles?
For a party, you can spend no more than $12 on nuts. Peanuts cost $2/lb. Cashews cost $4/lb. What are three possible combinations of peanuts and cashews you can buy?
Problem 5: Writing an Inequality From a Graph
What is the inequality that represents the graph?
What is the inequality that represents the graph?