Chapter 2 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. The...

Chapter 2 Section 2

Objectives

1

Copyright © 2012, 2008, 2004 Pearson Education, Inc.

The Multiplication Property of Equality

Use the multiplication property of equality.

Simplify, and then use the multiplication property of equality.

2.2

2


Objective 1


Slide 2.2-3


The addition property of equality is not enough to solve some equations, such as

Since the coefficient of x is 3 rather than 1, the multiplication property of equality is needed to change the equation to the form x = a number, after the 2 is subtracted from both sides of the equation and we are left with

3 2 17.x

3 15.x

Multiplication Property of EqualityIf A, B, and C (C ≠ 0) represent real numbers, then the equations

and are equivalent equations.

That is, we can multiply each side of an equation by the same nonzero number without changing the solution.

A B AC BC

Slide 2.2-4



Just as the addition property of equality permits subtracting the same number from each side of an equation, the multiplication property of equality permits dividing each side of an equation by the same number.

DO NOT, however, divide each side by a variable, since the variable might be equal to 0.

This property can be used to solve . The on the left must be

changed to 1x, or x. To isolate x, we multiply each side of the equation

by , the reciprocal of 3, which will result in a coefficient of 1 when

multiplied.

3 15x 3x

1 33 1

3 3

1

3

Slide 2.2-5

Use the multiplication property of equality. (cont’d)

It is usually easier to multiply on each side if the coefficient of the variable is a fraction, and divide on each side if the coefficient is an integer.


Solve.

Solution:

15 1

5

5

1 75x

5x

15 75x

Check:

15(5) 75

75 75

The solution set is 5 .

Slide 2.2-6

EXAMPLE 1 Applying the Multiplication Property of Equality


Solve.

Solution:

8 2

8 8

0x

5

2x

8 20x

Check:

8 05

22

20 20

The solution set is5

.2

8 20x

Slide 2.2-7



Solve.

Solution:

0.7 5.04.x

0.7

0.7 4

0.7

5.0x

7.2x

Check:

7.20.7 5.04

5.04 5.04

0.7 5.04x

The solution set is 7.2 .

Slide 2.2-8

EXAMPLE 3 Solving an Equation with Decimals


Solution:

Solve.

64

x

4 464

x

24x 624

4

64

x

6 6

Check:


Slide 2.2-9



Solve.

18t (18

22

3) 1

12 12

212

3t

Solution:

212

3 3

2 23t

Check:

212

3t


Slide 2.2-10



Using the multiplication property of equality when the coefficient of the variable is −1.In Section 2.1, we obtained the equation We reasoned that since this equation says that the additive inverse (or opposite) of x is −17, then x must equal 17. We can also use the multiplication property of equality to obtain the same result as detailed in the next example.

17.x

Slide 2.2-11


Solution:

71 p

1 7p

( 7) 7

Solve. 7p

71 11 p

1( 1) 7p

7p

Check:

7p

7 7


Slide 2.2-12



Objective 2

Simplify, and then use the multiplication property of equality.

Slide 2.2-13


Solve.

4 9 20r r

5 20

5 5

r

Solution:

5 20r

4r

4 9 20r r

Check:


( 4) ( 4)4 9 20 16 ( 36) 20

20 20

Slide 2.2-14

EXAMPLE 7 Combing Like Terms When Solving

Chapter 2 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. The...

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