solving equations (algebra 2)
DESCRIPTION
Students review properties of equality, used for solving equations.TRANSCRIPT
![Page 1: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/1.jpg)
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Solving Equations Solving Equations
1) open sentence2) equation3) solution
Translate verbal expressions into algebraic expression and equations and vice versa. Solve equations using the properties of equality.
![Page 3: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/3.jpg)
A mathematical sentence (expression) containing one or more variables is called an open sentence.
Solving Equations Solving Equations
![Page 4: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/4.jpg)
A mathematical sentence (expression) containing one or more variables is called an open sentence.
A mathematical sentence stating that two mathematical expressions are equalis called an _________.
Solving Equations Solving Equations
![Page 5: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/5.jpg)
A mathematical sentence (expression) containing one or more variables is called an open sentence.
A mathematical sentence stating that two mathematical expressions are equalis called an _________.equation
Solving Equations Solving Equations
![Page 6: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/6.jpg)
A mathematical sentence (expression) containing one or more variables is called an open sentence.
A mathematical sentence stating that two mathematical expressions are equalis called an _________.equation
Open sentences are neither true nor false until the variables have been replaced by numbers.
Solving Equations Solving Equations
![Page 7: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/7.jpg)
A mathematical sentence (expression) containing one or more variables is called an open sentence.
A mathematical sentence stating that two mathematical expressions are equalis called an _________.equation
Open sentences are neither true nor false until the variables have been replaced by numbers.
Each replacement that results in a true statement is called a ________ of theopen sentence.
Solving Equations Solving Equations
![Page 8: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/8.jpg)
Solving Equations Solving Equations
A mathematical sentence (expression) containing one or more variables is called an open sentence.
A mathematical sentence stating that two mathematical expressions are equalis called an _________.equation
Open sentences are neither true nor false until the variables have been replaced by numbers.
Each replacement that results in a true statement is called a ________ of theopen sentence.
solution
![Page 9: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/9.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Solving Equations Solving Equations
![Page 10: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/10.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
Solving Equations Solving Equations
![Page 11: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/11.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
Solving Equations Solving Equations
![Page 12: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/12.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,– 5 + y = – 5 + y
Solving Equations Solving Equations
![Page 13: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/13.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
For all real numbers a and b,
If a = b, then b = a
– 5 + y = – 5 + y
Solving Equations Solving Equations
![Page 14: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/14.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
For all real numbers a and b,
If a = b, then b = a
– 5 + y = – 5 + y
If 3 = 5x – 6, then 5x – 6 = 3
Solving Equations Solving Equations
![Page 15: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/15.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
For all real numbers a and b,
If a = b, then
For all real numbers a, b, and c.
If a = b, and b = c, then
b = a
a = c
– 5 + y = – 5 + y
If 3 = 5x – 6, then 5x – 6 = 3
Solving Equations Solving Equations
![Page 16: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/16.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
For all real numbers a and b,
If a = b, then
For all real numbers a, b, and c.
If a = b, and b = c, then
b = a
a = c
– 5 + y = – 5 + y
If 3 = 5x – 6, then 5x – 6 = 3
If 2x + 1 = 7 and 7 = 5x – 8
then, 2x + 1 = 5x – 8
Solving Equations Solving Equations
![Page 17: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/17.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
For all real numbers a and b,
If a = b, then
For all real numbers a, b, and c.
If a = b, and b = c, then
If a = b, then a may be replacedby b and b may be replaced by a.
b = a
a = c
– 5 + y = – 5 + y
If 3 = 5x – 6, then 5x – 6 = 3
If 2x + 1 = 7 and 7 = 5x – 8
then, 2x + 1 = 5x – 8
Solving Equations Solving Equations
![Page 18: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/18.jpg)
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Properties of Equality Property Symbol Example
Reflexive
Symmetric
Transitive
Substitution
For any real number a,
a = a,
For all real numbers a and b,
If a = b, then
For all real numbers a, b, and c.
If a = b, and b = c, then
If a = b, then a may be replacedby b and b may be replaced by a.
b = a
a = c
– 5 + y = – 5 + y
If 3 = 5x – 6, then 5x – 6 = 3
If 2x + 1 = 7 and 7 = 5x – 8
then, 2x + 1 = 5x – 8
If (4 + 5)m = 18
then 9m = 18
Solving Equations Solving Equations
![Page 19: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/19.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Solving Equations Solving Equations
![Page 20: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/20.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
Solving Equations Solving Equations
![Page 21: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/21.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b+ c + c
Solving Equations Solving Equations
![Page 22: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/22.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b+ c + c a = b- c - c
Solving Equations Solving Equations
![Page 23: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/23.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b+ c + c a = b- c - c
Example:
If x – 4 = 5, then
Solving Equations Solving Equations
![Page 24: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/24.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b+ c + c a = b- c - c
Example:
If x – 4 = 5, then x – 4 = 5+ 4 + 4
Solving Equations Solving Equations
![Page 25: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/25.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b+ c + c a = b- c - c
Example:
If x – 4 = 5, then x – 4 = 5+ 4 + 4
If n + 3 = –11, then
Solving Equations Solving Equations
![Page 26: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/26.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Addition and Subtraction Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b+ c + c a = b- c - c
Example:
If x – 4 = 5, then x – 4 = 5+ 4 + 4
If n + 3 = –11, then n + 3 = –11– 3 – 3
Solving Equations Solving Equations
![Page 27: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/27.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Solving Equations Solving Equations
![Page 28: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/28.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
Solving Equations Solving Equations
![Page 29: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/29.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b· c · c
Solving Equations Solving Equations
![Page 30: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/30.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b· c · c a = b c c
Solving Equations Solving Equations
![Page 31: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/31.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b· c · c a = b
Example:
c c
then64m
If
Solving Equations Solving Equations
![Page 32: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/32.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b· c · c a = b
Example:
4 4
c c
then64m
If 6 4m
Solving Equations Solving Equations
![Page 33: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/33.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b· c · c a = b
Example:
4 4
c c
then64m
If 6 4m then6y3 If -
Solving Equations Solving Equations
![Page 34: Solving Equations (Algebra 2)](https://reader034.vdocuments.site/reader034/viewer/2022051322/5467f274af7959f9288b5887/html5/thumbnails/34.jpg)
Sometimes an equation can be solved by adding the same number to each side or bysubtracting the same number from each side or by multiplying or dividing each side by the same number.
Multiplication and Division Properties of Equality
For any real numbers a, b, and c, if a = b, then
a = b· c · c a = b
Example:
4 4
c c
then64m
If 6 4m then6y3 If - 6 3 y
-3 -3
Solving Equations Solving Equations
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Java Applet – Solving Functions
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Credits Credits
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Using Glencoe’s Algebra 2 text,© 2005