Linear Equations and Inequalities in One Variable What is an equation? =

Linear Equations and Inequalities in One Variable

What is an equation?

=

Linear Equations and Inequalities in One Variable

What is an equation?

Linear Equations and Inequalities in One Variable

What is an equation?

Linear Equations and Inequalities in One Variable

What is an equation?

Properties of Equality

Reflexive Property

a = a

Properties of Equality

Symmetric Property

If a = b then b = a

Properties of Equality

Transitive Property

If a = b and b = c then a = c

Properties of Equality

Addition Property

If a = b then a + c = b + c

Properties of Equality

Subtraction Property

If a = b then a - c = b - c

Properties of Equality

Multiplication Property

If a = b then ac = bc

Properties of Equality

Division Property

If a = b and c = 0 then a/c = b/c

Properties of Equality

Whatever you do to

one side of an equation

Properties of Equality

do the same thing to the other side

Properties of Equality

and the two sides will stay equal

Examples

n – 6 = 9

Examples

n – 6 = 9Add 6 to both sides(addition property)

Examples

n – 6 = 9 +6 +6

Examples

n – 6 = 9 +6 +6 n = 3

Examples

n = 3

Examples

-35 = -5r

Examples

-35 = -5rDivide both sides by -5

(division property)

Examples

-35 = -5r -5 -5

Examples

7 = r

Examples

-3(m + 3) = 16

Examples

-3(m + 3) = 16

Distribute to get the m out of the parentheses

Examples

-3(m + 3) = 16-3m - 9 = 16

Distribute to get the m out of the parentheses

Examples

-3(m + 3) = 16-3m - 9 = 16

Add 9 to both sides(addition property)

Examples

-3(m + 3) = 16-3m - 9 = 16

+9 +9

Examples

-3(m + 3) = 16-3m - 9 = 16

+9 +9 -3m = 25

Examples

-3(m + 3) = 16-3m - 9 = 16

+9 +9 -3m = 25

Divide both sides by -3(division property)

Examples

-3m = 25 -3 -3

Examples

m = -25 3

Examples

4s + 6s = 100

Examples

4s + 6s = 100

Combine like terms

Examples

4s + 6s = 10010s = 100

Combine like terms

Examples

4s + 6s = 10010s = 100

Divide each side by 10(division property)

Examples

4s + 6s = 10010s = 100

10 10

Examples

s = 10

Examples

12 + 2g = 4 + 6g

Examples

12 + 2g = 4 + 6gMove the variable to one

side of the equation

Examples

12 + 2g = 4 + 6g -2g -2g

(subtraction property)

Examples

12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g

Examples

12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4gSubtract 4 from both sides

(subtraction property)

Examples

12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g

Examples

12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g

Divide both sides by 4

Examples

12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g 4 4

Examples

2 = g

Today’s Work:

Page 45Problems 7-20

When you finish, you may work quietly on any homework you have.