1 5 Open Sentences Objective To solve open

1 -5 Open Sentences Objective: To solve open sentences by performing arithmetic operations.

Drill #6 1. 2. 3.

Open Sentences** Definition: Mathematical statements with one or more variables or unknowns. Examples: 2 x + 6 = 5 3 x > 7

Solution** Definition: The replacement of a variable that results in a true sentence is the solution of that sentence. 3 is a solution to 3 x + 6 = 15 4 is a solution to 4 x > 10

Sets and elements … • A set is a collection of objects or numbers. • Sets are enclosed by braces { } • Each object or number in a set is called an element. Example: {-1, 0, 1, 2, 3}

Replacement Set** Definition: The set of numbers from which replacements for a variable may be chosen. Example: To follow

Solution Set** Definition: The set of all replacements from the replacement set, which are a solution for the open sentence. Example: To follow

Use the replacement set {3, 4, 5, 6} to find a solution set for 6 b + 7= 37 Replace b with 6 b + 7 = 37 True or False? 3 6(3) + 7 = 25 False 4 6(4) + 7 = 31 False 5 6(5) + 7 = 37 True 6 6(6) + 7 = 43 False

Find the solution set for y + 5 < 7 if the replacement set is {0, 1, 2, 3, 4} Replace y with: 0 y+5<7 True or False 0+5=5<7 True 1 1+5=6<7 True 2 2+5=7<7 True 3 3+5=8<7 False 4 4+5=9<7 False

Equality and Inequality** Equation (equality): A sentence that contains an equals sign (=). Inequality: A sentence having the symbols < , > , or > Mathematical Sentence Equation or inequality 2 x + 10 = 50 Equality 3 a < 20 Inequality y – 6 > 12 Inequality

Find the solution set What is the solution set for the inequality 2 x + 5 < 10 if the replacement set is {0, ½, 1, 2, 3} Answer: {0, ½, 1, 2}

Quiz Topics 1 -1 Variables and Expressions 1 -2 Patterns and Sequences 1 -3 Order of Operations