The document defines key terms related to open sentences including: - Open sentence: A mathematical statement with one or more variables - Solution: The replacement value for a variable that makes an open sentence true - Replacement set: The set of numbers that can replace a variable - Solution set: The set of elements from the replacement set that make an open sentence true Examples are provided to demonstrate finding the solution set of equations and inequalities given a replacement set. The document notes that solution sets do not have to be numbers and can include other types of values.

1. Open Sentences

2. What You'll Learn Vocabulary 1) open sentence 2) solving an open sentence 3) solution 4) equation 5) replacement set Open Sentences Solve open sentence equations. Solve open sentence inequalities. 6) set 7) element 8) solution set 9) inequality

3. Open Sentences The Homeowners Association is planning a community-wide garage sale, and their advertising budget is $135.

4. Open Sentences The Homeowners Association is planning a community-wide garage sale, and their advertising budget is $135. The expression 15.50 + 5 n can be used to represent the cost of purchasing n + 1 kits.

5. Open Sentences The Homeowners Association is planning a community-wide garage sale, and their advertising budget is $135. The expression 15.50 + 5 n can be used to represent the cost of purchasing n + 1 kits. The open sentence, 15.50 + 5n < 135 can be used to ensure that the budget is met.

6. Open Sentences A mathematical statement with one or more variables is called an _____________.

7. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence

8. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values.

9. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values. The process of finding a value for a variable that results in a true sentence is called _______________________.

10. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values. The process of finding a value for a variable that results in a true sentence is called _______________________. solving the open sentence

11. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values. The process of finding a value for a variable that results in a true sentence is called _______________________. solving the open sentence The replacement value is called a ________ of the open sentence.

12. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values. The process of finding a value for a variable that results in a true sentence is called _______________________. solving the open sentence The replacement value is called a ________ of the open sentence. solution

13. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values. The process of finding a value for a variable that results in a true sentence is called _______________________. solving the open sentence The replacement value is called a ________ of the open sentence. solution A sentence that contains an equals sign =, is called an _________.

14. Open Sentences A mathematical statement with one or more variables is called an _____________. open sentence An open sentence is neither true nor false until the variables have been replaced by specific values. The process of finding a value for a variable that results in a true sentence is called _______________________. solving the open sentence The replacement value is called a ________ of the open sentence. solution A sentence that contains an equals sign =, is called an _________. equation

15. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________.

16. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set

17. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers.

18. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers. set

19. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers. A set is often shown using brackets { } and is usually name by a capital letter. set

20. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers. A set is often shown using brackets { } and is usually name by a capital letter. Each object or number in the set is called an ________, or member. set

21. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers. A set is often shown using brackets { } and is usually name by a capital letter. Each object or number in the set is called an ________, or member. element set

22. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers. A set is often shown using brackets { } and is usually name by a capital letter. Each object or number in the set is called an ________, or member. element set The ____________ of an open sentence is the set of elements from the replacement set that make an open sentence true .

23. Open Sentences A set of numbers from which replacements for a variable may be chosen is called a ________________. replacement set A ____ is a collection of objects or numbers. A set is often shown using brackets { } and is usually name by a capital letter. solution set Each object or number in the set is called an ________, or member. element The ____________ of an open sentence is the set of elements from the replacement set that make an open sentence true . set

24. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }.

25. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. True or False 6n + 7 = 37 n

26. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. 3 6( 3 ) + 7 = 37 False True or False 6n + 7 = 37 n

27. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. 3 6( 3 ) + 7 = 37 False 4 6( 4 ) + 7 = 37 False True or False 6n + 7 = 37 n

28. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. 3 6( 3 ) + 7 = 37 False 4 6( 4 ) + 7 = 37 False 5 6( 5 ) + 7 = 37 True True or False 6n + 7 = 37 n

29. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. 3 6( 3 ) + 7 = 37 False 4 6( 4 ) + 7 = 37 False 5 6( 5 ) + 7 = 37 True 6 6( 6 ) + 7 = 37 False True or False 6n + 7 = 37 n

30. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. 3 6( 3 ) + 7 = 37 False 4 6( 4 ) + 7 = 37 False 5 6( 5 ) + 7 = 37 True 6 6( 6 ) + 7 = 37 False 7 6( 7 ) + 7 = 37 False True or False 6n + 7 = 37 n

31. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is { 3, 4, 5, 6, 7 }. The solution set is: 3 6( 3 ) + 7 = 37 False 4 6( 4 ) + 7 = 37 False 5 6( 5 ) + 7 = 37 True 6 6( 6 ) + 7 = 37 False 7 6( 7 ) + 7 = 37 False { 5 } True or False 6n + 7 = 37 n

32. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is

33. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is True or False

34. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is True or False

35. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is True or False

36. Open Sentences Example: Use a Replacement Set to Solve an Equation Find the solution set for the equation if the replacement set is True or False

37. Open Sentences Example: Use a Replacement Set to Solve an Equation The solution set is: Find the solution set for the equation if the replacement set is True or False

38. Open Sentences An open sentence that contains the symbol is called an ___________.

39. Open Sentences inequality An open sentence that contains the symbol is called an ___________.

40. Open Sentences inequality An open sentence that contains the symbol is called an ___________. Study Tip Reading Math Inequality symbols are read as follows. is less than is less than or equal to is greater than is greater than or equal to

41. Open Sentences Example: Find the Solution Set of an Inequality Find the solution set for the inequality if the replacement set is

42. Open Sentences Example: Find the Solution Set of an Inequality True or False Find the solution set for the inequality if the replacement set is

43. Open Sentences Example: Find the Solution Set of an Inequality 7 18 – 7 < 10 False True or False Find the solution set for the inequality if the replacement set is

44. Open Sentences Example: Find the Solution Set of an Inequality 7 18 – 7 < 10 False 8 18 – 8 < 10 False True or False Find the solution set for the inequality if the replacement set is

45. Open Sentences Example: Find the Solution Set of an Inequality 7 18 – 7 < 10 False 8 18 – 8 < 10 False 9 18 – 9 < 10 True True or False Find the solution set for the inequality if the replacement set is

46. Open Sentences Example: Find the Solution Set of an Inequality 7 18 – 7 < 10 False 8 18 – 8 < 10 False 9 18 – 9 < 10 True 10 18 – 10 < 10 True True or False Find the solution set for the inequality if the replacement set is

47. Open Sentences Example: Find the Solution Set of an Inequality 7 18 – 7 < 10 False 8 18 – 8 < 10 False 9 18 – 9 < 10 True 10 18 – 10 < 10 True 11 18 – 11 < 10 True True or False Find the solution set for the inequality if the replacement set is

48. Open Sentences Example: Find the Solution Set of an Inequality The solution set is: 7 18 – 7 < 10 False 8 18 – 8 < 10 False 9 18 – 9 < 10 True 10 18 – 10 < 10 True 11 18 – 11 < 10 True { 9, 10, 11 } True or False Find the solution set for the inequality if the replacement set is

49. Open Sentences As mentioned earlier, solution sets do not have to be numbers. Here’s an example: Consider the following open sentence. It is the name of a month between March and July.

50. Open Sentences As mentioned earlier, solution sets do not have to be numbers. Here’s an example: Consider the following open sentence. It is the name of a month between March and July. Your replacement set is

51. Open Sentences As mentioned earlier, solution sets do not have to be numbers. Here’s an example: Consider the following open sentence. It is the name of a month between March and July. Your replacement set is { January, February, March, April, May, June, July, August, September, October, November, December } Your solution set is

52. Open Sentences As mentioned earlier, solution sets do not have to be numbers. Here’s an example: Consider the following open sentence. It is the name of a month between March and July. Your replacement set is { January, February, March, April, May, June, July, August, September, October, November, December } Your solution set is { April, May, June }

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