Transcript Addition Principle of Equality and Inequality
Slide 1
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 2
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 3
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 4
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 5
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 2
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 3
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 4
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5
Slide 5
Addition Principle of Equality
and Inequality
Copyrighted © by T. Darrel Westbrook
Addition Principle of Equality and Inequality
Algebraic transformations are accomplished by using principles of
relationships and properties of numbers to mathematically change
the appearance of mathematical expressions, equations, and
inequalities.
Expressions, equations, and inequalities are considered as one entity,
except as noted in the presentation.
31 October 2015
Addition Principle of Equality and Inequality
2
Addition Principle of Equality and Inequality
Definition: Addition Principle of Equality – if a = b and a Real
Number c, then a c = b c.
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide two specific examples of this principle?
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
3
Addition Principle of Equality and Inequality
Definition: Addition Principle of Inequality – if a > b and a Real
Number c, then a c > b c. (Note: the inequality
symbols can be any of , , , , or as long as they are
consistent).
What does this mean?
Is it always true?
How can you use it in an Algebra class?
Provide a specific example for each of the inequality symbols.
What is a general example of this principle?
31 October 2015
Addition Principle of Equality and Inequality
4
Addition Principle of Equality and Inequality
End of Line
31 October 2015
Addition Principle of Equality and Inequality
5