Open Sentences (Algebra1 1_3)

1) open sentence2) solving an open sentence3) solution4) equation5) replacement set

Open Sentences Open Sentences

Solve open sentence equations.

Solve open sentence inequalities.

6) set7) element8) solution set9) inequality


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



The expression 15.50 + 5n can be used torepresent the cost of purchasing n + 1 kits.



The expression 15.50 + 5n can be used torepresent the cost of purchasing n + 1 kits.

The open sentence, 15.50 + 5n < 135 can beused to ensure that the budget is met.


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


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 byspecific values.




The process of finding a value for a variable that results in a true sentence is called_______________________.




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.





The replacement value is called a ________ of the open sentence.solution






A sentence that contains an equals sign =, is called an _________.






A sentence that contains an equals sign =, is called an _________.equation


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


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 ____ is a collection of objects or numbers. set




A set is often shown using brackets { } and is usually name by a capital letter.

set





Each object or number in the set is called an ________, or member.

set





Each object or number in the set is called an ________, or member.element

set






set

The ____________ of an open sentence is the set of elements from the replacementset that make an open sentence true.





solution set


The ____________ of an open sentence is the set of elements from the replacementset that make an open sentence true.

set


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 }.

3776 n




3776 n

n 6n + 7 = 37 True or False




3776 n


3 6(3) + 7 = 37 False




3776 n


3 6(3) + 7 = 37 False

4 6(4) + 7 = 37 False




3776 n


3 6(3) + 7 = 37 False

4 6(4) + 7 = 37 False

5 6(5) + 7 = 37 True




3776 n


3 6(3) + 7 = 37 False

4 6(4) + 7 = 37 False

5 6(5) + 7 = 37 True

6 6(6) + 7 = 37 False




3776 n


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




3776 n


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 }



1225

127 x

Find the solution set for the equation if the replacement set is

2

3 ,1 ,

2

1



1225

127 x

True or False


2

3 ,1 ,

2

1

1225

127 xx



1225

127 x

True or False


2

3 ,1 ,

2

1

1225

127 xx

False 12

25

12

7

12

6

2

1



1225

127 x

True or False


2

3 ,1 ,

2

1

1225

127 xx

False 12

25

12

7

12

6

2

1

False 12

25

12

7

12

12 1



1225

127 x

True or False


2

3 ,1 ,

2

1

1225

127 xx

False 12

25

12

7

12

6

2

1

False 12

25

12

7

12

12 1

True 12

25

12

7

12

18

2

3



1225

127 x

True or False



2

3 ,1 ,

2

1

1225

127 xx

False 12

25

12

7

12

6

2

1

False 12

25

12

7

12

12 1

True 12

25

12

7

12

18

2

3

2

3


An open sentence that contains the symbol is called an ___________. or , ,


An open sentence that contains the symbol is called an ___________. or , , inequality


An open sentence that contains the symbol is called an ___________. or , , inequality

Study Tip

Reading MathInequality symbolsare read as follows.

is less than

is less than or equal to

is greater than

is greater than or equal to


Example: Find the Solution Set of an Inequality

1018 y

Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7



1018 y

True or False


1018 yy



1018 y

True or False


1018 yy

7 18 – 7 < 10 False



1018 y

True or False


1018 yy

7 18 – 7 < 10 False

8 18 – 8 < 10 False



1018 y

True or False


1018 yy

7 18 – 7 < 10 False

8 18 – 8 < 10 False

9 18 – 9 < 10 True



1018 y

True or False


1018 yy

7 18 – 7 < 10 False

8 18 – 8 < 10 False

9 18 – 9 < 10 True

10 18 – 10 < 10 True



1018 y

True or False


1018 yy

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



1018 y

True or False



1018 yy

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 }


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





Your replacement set is { January, February, March, April, May, June, July, August, September, October, November, December }

Your solution set is





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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Open Sentences (Algebra1 1_3)