1
2.2

• The Addition and Multiplication Properties of
  Equality

2
Linear Equations

• Linear equations in one variable
• can be written in the form ax b c,
• where a, b and c are real numbers, and a ? 0.
• Equivalent equations
• are equations that have the same solution.

3
Addition Property of Equality
Addition Property of Equality
If a, b, and c are real numbers, then a b
and a c b c are equivalent equations.
Example
z 16 Simplify both sides.
4
Solving Equations
Example
4p 11 p 2 2p 20
3p 11 2p 18 (Simplify both sides.)
p 11 18 Simplify both sides.
p 7 Simplify both sides.
5
Solving Equations
Example
5(3 z) (8z 9) 4z
15 5z 8z 9 4z Use distributive
property.
6 3z 4z Simplify left side.
6 z 0 Simplify both sides.
z 6 Simplify both sides.
6
Word Phrases as Algebraic Expressions
Example
Write the following sentence as an equation.
The product of 5 and 29 gives 145.
In words
The product of
and 29
gives
145
5
Translate
( 5)
( 29)


145
7
Multiplication Property of Equality

• Multiplication Property of Equality
• If a, b, and c are real numbers and c ? 0, then
• a b and ac bc
• are equivalent equations.

Example
y 8
y 8 Simplify both sides.
8
Solving Equations
Example
9
Solving Equations
Example
10
Using Both Properties
Example
3z 1 26
3z 27 Simplify both sides.
z 9 Simplify both sides.
11
Using Both Properties
Example
12x 30 8x 6 10
20x 24 10 Simplify the left side.
20x 14 Simplify both sides.