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

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Open Sentences** Definition: Mathematical statements with one or more variables or unknowns. Examples: 2x + 6 = 5 3x > 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 3x + 6 = 15 4 is a solution to 4x > 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 6b + 7= 37 Replace b with6b + 7 = 37True or False? 36(3) + 7 = 25False 46(4) + 7 = 31False 56(5) + 7 = 37True 66(6) + 7 = 43False

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

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

Find the solution set What is the solution set for the inequality 2x + 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