4 minutes Warm-Up Fill in each blank with <, >, or = to make each statement true. 1) 2___3 5) 5___ 2) 5___4 6) -2___-5 3) 3___-1 7) 4) -7___-4

2.1Inequalities and Their Graphs Objectives: To determine whether a number is a solution of an inequality To graph inequalities on the number line

Inequalities “is less than” “is greater than” “is less than or equal to” “is greater than or equal to”

Example 1 Determine whether each number is a solution of a) 3 yes, because 3 is less than 7 b) -2 yes, because -2 is less than 7 c) 9 no, because 9 is not less than or equal to 7 d) 7 yes, because 7 is equal to 7

Example 2 Graph x > 5 on a number line. 3 4 5 6 7

Example 3 Graph on a number line. -3 -2 -1 1

Practice Graph on a number line. 1) 2)

2.2 The Addition Property of Inequalities Objectives: To solve inequalities using the addition property

Properties of Inequality For all real numbers a,b, and c, where Addition Property Subtraction Property

Example 1 Solve and graph the solution set. -7 -7 1 2 3 4

Practice Solve each inequality and graph the solution. 1) 2)

Example 2 Solve and graph the solution set. -6 -6 8 9 10 11 12

Practice Solve each inequality and graph the solution. 1) 2)

Example 3 Solve and graph the solution set. -1 1 2 3

Practice Solve each inequality and graph the solution. 1) 2)

3.3 The Multiplication Property of Inequalities Objectives: To solve inequalities using the multiplication property

Anytime you multiply or divide by a negative number “flip” the inequality sign to make it true.

Example 1 Solve and graph the solution. 7 7 1 2 3 4 5

Example 2 Solve and graph the solution. -5 -5 -9 -8 -7 -6 -5

Example 3 Solve and graph the solution. -2 -1 1 2