Solving Equations (Algebra 2)

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Open sentences are neither true nor false until the variables have been replaced by numbers.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Open sentences are neither true nor false until the variables have been replaced by numbers.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Open sentences are neither true nor false until the variables have been replaced by numbers.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