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Students review properties of equality, used for solving equations.
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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.
A mathematical sentence (expression) containing one or more variables is called an open sentence.
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 _________.
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
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Open sentences are neither true nor false until the variables have been replaced by numbers.
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Open sentences are neither true nor false until the variables have been replaced by numbers.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.
Solving Equations Solving Equations
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Open sentences are neither true nor false until the variables have been replaced by numbers.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
To solve equations, we can use properties of equality.Some of these equivalence relations are listed in the following table.
Solving Equations Solving Equations
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Java Applet – Solving Functions
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Using Glencoe’s Algebra 2 text,© 2005