Algebra 1 Common Core Student Edition, Grade 8-9

You can use the M ultiplication and D ivision Properties o f Equality to solve equations.

Division is the inverse of multiplication.

Pr o p er t y Multiplication and Division Properties of Equality

Multiplication Property of Equality M u l t i p l y i n g e a c h s id e o f a n e q u a t io n b y th e

s a m e n o n z e r o n u m b e r p r o d u c e s a n e q u iv a le n t e q u a t io n.

Algebra Example

F o r a n y r e a l n u m b e r s a, b, and c, X _ r, 3 z

iia = b, th e n a • c = b • c. | • 3 = 2 • 3y

Division Property of Equality Dividing each side of an equation by the same nonzero

num ber produces an equivalent equation.

Algebra Example

For any real num bers a, b, and c, such 5x = 20

that c 0 , i f a = b, then § = 5x^20

5 5

V J

How can a model
help you solve the
equation?
The model tells you that
you must divide 6.4 by
4 in order to solve the
equation Ax = 6.4.

i.'

Pr o b l em 3 Solving an Equation Using Division I6R.IDDED RESPONSE

What is the solution of Ax = 6.4?

Ax = 6.4

Ax 6.4

4 , Divide each side by 4.

x=1.6 Simplify.

Got It? 3. W h a t is t h e s o lu t io n o f e a c h e q u a tio n? C h e c k y o u r a n s w e r,

a. 10 = 1 5 * b. -3 .2 z = 14

Pr o b l em 4 Solving an Equation Using Multiplication

What is the solution of | = — 9?

Pl an _
How can a model
help you solve the
equation?
The model tells you that
you must multiply - 9
by 4 in order to solve the
equation \ = -9.

y x........i

I -9 I -9 I -9 I - n G o t It? 4. What is the solution of each equation? Check your answer.

x

4

% = —9

4= -9 • 4

x = - 3 6

M u ltip ly each side by 4.

Simplify.

19 = 5 b.^ = 8

j L e s s o n 2 - 1 So l v i n g O n e - St e p Eq u a t i o n s □ 83

V-------------------------------------V---------------------------------------------------------------------