3/29/07 Ms. Waters

3/29/07 Ms. Waters

Objectives

• To apply the properties of equality• To simplify expressions using addition, subtraction, multiplication and division.• To solve simple multi-step equations. Sunshine State Standards

• MA.A.3.3.1• MA.D.2.3.1• MA.D.2.3.2

3/29/07 Ms. Waters

To solve two-step equations, you want to get the variable alone on one side of the equal sign using properties of equality and inverse operations.

Vocabulary:

Addition Property of Equality-If you add the same value to each side of an equation, the two sides remain equal.

€

x = 7, so x + 3 = 7 + 3

x + 3 =10

3/29/07 Ms. Waters

€

x = 6, so x − 4 = 6 − 4

x − 4 = 2

Subtraction Property of EqualityIf you subtract the same value from each side of an equation, the two sides remain equal. If a = b, then a - c = b - c

Vocabulary

3/29/07 Ms. Waters

Vocabulary

Multiplication Property of EqualityIf you multiply each side of an equation by the same number, the two sides remain equal.

€

x =10 so, x • 5 =10• 5

x • 5 = 50

3/29/07 Ms. Waters

Vocabulary

Division Property of EqualityIf you divide each side of an equation by the same nonzero number, the two sides remain equal. If a = b, then a = b

c c

€

x =16, sox

2=16

2x

2= 8

3/29/07 Ms. Waters

Lets practice the properties we just learned about.

€

x = 8

€

x • 2 = 8• 2

€

2x =16

€

2x −5 =16 −5

€

2x −5 =11

€

x =12

€

x

6=12

6

€

x

6= 2

€

x

6+ 4 = 2 + 4

€

x

6+ 4 = 6

€

x = 5

€

x • 3 = 5• 3

€

3x =15

€

3x +1=15 +1

€

3x +1=16Check

Check

Check

3/29/07 Ms. Waters

Vocabulary

Inverse OperationsOperations that undo each other. - is the inverse operation of?÷ is the inverse operation of?

+x

3/29/07 Ms. Waters

The order of solving a two-step equation is the reverse of the order of operations.

First undo addition or subtraction

€

2x + 3 =11

€

−3 − 3

€

2x = 8Then, undo multiplication or division

€

2x

2=8

2

€

x = 4

3/29/07 Ms. Waters

What would the previous equation look like if weused physical models to express it?

Remember:

= 0+

2x€

2x + 3 =11

€

2x

2

x = 4