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Students are introduced to open sentences and inequalities.
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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
Open Sentences Open Sentences
The Homeowners Association is planning a community-wide garage sale, and their advertising budget is $135.
Open Sentences Open Sentences
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.
Open Sentences Open Sentences
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 open sentence, 15.50 + 5n < 135 can beused to ensure that the budget is met.
Open Sentences Open Sentences
A mathematical statement with one or more variables is called an _____________.
Open Sentences Open Sentences
A mathematical statement with one or more variables is called an _____________.open sentence
Open Sentences 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 byspecific values.
Open Sentences 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 byspecific values.
The process of finding a value for a variable that results in a true sentence is called_______________________.
Open Sentences 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 byspecific values.
The process of finding a value for a variable that results in a true sentence is called_______________________.solving the open sentence
Open Sentences 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 byspecific 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.
Open Sentences 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 byspecific 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
Open Sentences 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 byspecific 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 _________.
Open Sentences 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 byspecific 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
Open Sentences Open Sentences
A set of numbers from which replacements for a variable may be chosen is called a ________________.
Open Sentences Open Sentences
A set of numbers from which replacements for a variable may be chosen is called a ________________.replacement set
Open Sentences 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.
Open Sentences 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
Open Sentences 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
Open Sentences 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
Open Sentences 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
Open Sentences 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 replacementset that make an open sentence true.
Open Sentences 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 replacementset that make an open sentence true.
set
Open Sentences 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 }.
3776 n
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
3 6(3) + 7 = 37 False
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
3 6(3) + 7 = 37 False
4 6(4) + 7 = 37 False
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
3 6(3) + 7 = 37 False
4 6(4) + 7 = 37 False
5 6(5) + 7 = 37 True
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
3 6(3) + 7 = 37 False
4 6(4) + 7 = 37 False
5 6(5) + 7 = 37 True
6 6(6) + 7 = 37 False
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
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
Open Sentences 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 }.
3776 n
n 6n + 7 = 37 True or False
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 }
Open Sentences Open Sentences
Example: Use a Replacement Set to Solve an Equation
1225
127 x
Find the solution set for the equation if the replacement set is
2
3 ,1 ,
2
1
Open Sentences Open Sentences
Example: Use a Replacement Set to Solve an Equation
1225
127 x
True or False
Find the solution set for the equation if the replacement set is
2
3 ,1 ,
2
1
1225
127 xx
Open Sentences Open Sentences
Example: Use a Replacement Set to Solve an Equation
1225
127 x
True or False
Find the solution set for the equation if the replacement set is
2
3 ,1 ,
2
1
1225
127 xx
False 12
25
12
7
12
6
2
1
Open Sentences Open Sentences
Example: Use a Replacement Set to Solve an Equation
1225
127 x
True or False
Find the solution set for the equation if the replacement set is
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
Open Sentences Open Sentences
Example: Use a Replacement Set to Solve an Equation
1225
127 x
True or False
Find the solution set for the equation if the replacement set is
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
Open Sentences Open Sentences
Example: Use a Replacement Set to Solve an Equation
1225
127 x
True or False
The solution set is:
Find the solution set for the equation if the replacement set is
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
Open Sentences Open Sentences
An open sentence that contains the symbol is called an ___________. or , ,
Open Sentences Open Sentences
An open sentence that contains the symbol is called an ___________. or , , inequality
Open Sentences Open Sentences
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
Open Sentences Open Sentences
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
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
1018 yy
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
1018 yy
7 18 – 7 < 10 False
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
1018 yy
7 18 – 7 < 10 False
8 18 – 8 < 10 False
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
1018 yy
7 18 – 7 < 10 False
8 18 – 8 < 10 False
9 18 – 9 < 10 True
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
1018 yy
7 18 – 7 < 10 False
8 18 – 8 < 10 False
9 18 – 9 < 10 True
10 18 – 10 < 10 True
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
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
Open Sentences Open Sentences
Example: Find the Solution Set of an Inequality
1018 y
True or False
The solution set is:
Find the solution set for the inequality if the replacement set is 11 0,1 ,9 ,8 ,7
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 }
Open Sentences 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.
Open Sentences 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
Open Sentences 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
Open Sentences 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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