copyright © 2014, 2010, 2006 pearson education, inc. section 2.2, slide 1 equations, inequalities,...

Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 2.2, Slide 1

Equations, Inequalities, and Applications2


1. Use the multiplication property of equality.

2. Simplify, and then use the multiplication property of equality.

Objectives

2.2 The Multiplication Property of Equality


Multiplication Property of EqualityIf A, B, and C (C is not equal to 0) represent real

numbers, then the equations

A = B and AC = BC

are equivalent equations.

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

Use the Multiplication Property of Equality


Divide each side by 3.

Example 1

Solve. 3x = 42

x = 14

Check: 3 · 14 = 42


3 42

3 3

x


NoteIn practice, 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 or a decimal. For example, to solve

it is easier to multiply by the reciprocal of than to

divide by On the other hand, to solve 5x = 20,it is easier to divide by 5 than to multiply by

312,

4 x

4

3 ,

3

4 ,

3.

4

1.

5



Example 3

Solve. –1.5y = 7.5

y = –5

Check: –1.5 · –5 = 7.5


Divide bothsides by –1.5.1.5

1.5 7.5=

1.5

y


Example 5

Solve.


53

6z

6

5

53

6

6

5z

18 or 3.6

5z

5 183

6 5Check:

Multiply each side by the reciprocal.


Example 7

Solve.

5a – 13a = 56

a = –7

Simplify and Use the Multiplication Property of Equality

8 56=

8 8

a

First combine like terms.

Then solve.

– 8a = 56

copyright © 2014, 2010, 2006 pearson education, inc. section 2.2, slide 1 equations, inequalities,...

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