Chapter 2 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Chapter Chapter 22Section Section 11

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


The Addition Property of Equality

11

33

22

2.12.12.12.1Identify linear equations.Use the addition property of equality.Simplify and then use the addition property of equality.


Objective 11

Slide 2.1 - 3

Identify linear equations.


Identify linear equations.

Slide 2.1 - 4

A linear equation in one variable can be written in the form

,

for real numbers A, B, and C, with A ≠ 0.

, , and are linear equations in one variable (x). The final two can be written in the specified form with the use of properties developed in this chapter.

Ax B C

4 9 0x 2 3 5x 7x

, , and

are not linear equations.

2 2 5x x 1

6x

2 6 0x

Linear Equations

Nonlinear Equations

Although x and y are typically used, other letters can be used for variables in equations.


Objective 22

Slide 2.1 - 5

Use the addition property of equality.


If A, B, and C are real numbers, then the equations

and are equivalent equations.

That is, we can add the same number to each side of an equation without changing the solution.

Use the addition property of equality.

To solve an equation, add the same number to each side. The addition property of equality justifies this step.

Slide 2.1 - 6

A B A C B C

Equations can be thought of in terms of a balance. Thus, adding the same quantity to each side does not affect the balance.


EXAMPLE 1

Slide 2.1 - 7

Solution:

Using the Addition Property of Equality

12 3x

122 3 121x 9x

9The solution set is .

Do NOT write the solution set as {x = 9}. This is incorrect notation. Simply write {9}.

Check:

12 3x 9 12 3

3 3

Solve .


EXAMPLE 2

Slide 2.1 - 8Slide 2.1 - 8

Solution:


4.14 . 13 4.1 .6m 2.2m

The solution set is .{ 2.2}

4.1 6.3m

Check: 4.1 6.3m 4.1 6.2 3.2 6.3 6.3

Solve .


The addition property of equality says that the same number may be added to each side of an equation.

Slide 2.1 - 9

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

The same number may be subtracted from each side of an equation without changing the solution.

In Section 1.5, subtraction was defined as addition of the opposite. Thus, we can also use the following rule when solving an equation.


EXAMPLE 3

Slide 2.1 - 10

Solution:


Solve .22 16x

22 116 166x

38 x

22 16x Check:

3822 16 22 22

The final line of the check does not give the solution to the problem, only a confirmation that the solution found is correct.

The solution set is .{ 38}


EXAMPLE 4

Slide 2.1 - 11

Solution:

Subtracting a Variable Expression

Solve .7 9

12 2

m m

1 m

7 91

2 2m m

Check:

7 2 9

2 2 21 1

9 9

2 2

The solution set is .{1}

7 91

7

22

7

22mm mm


Objective 33

Slide 2.1 - 12

Simplify and then use the addition property of equality.


EXAMPLE 5

Slide 2.1 - 13

Solution:

Simplifying an Equation before Solving

Solve .

113 4 12 12 424 4r rr r

9( ) 4( ) 4 9(0 0 0 0) 4 3( ) Check:

4 4


13 4 12 4r r

0r

9 4 6 2 9 4 3r r r r

9 4 6 2 9 4 3r r r r


EXAMPLE 6

Slide 2.1 - 14

Solution:

Using the Distributive Property to Simplify an Equation

Check:


4 4 3 5 1x x 1 11 1x

2x

4( 1) ( ) 12 3 2 5 4 3 6 5 1

12 11 1

Solve . 4 1 3 5 1x x

4 1 3 5 1x x

1 1

Be careful to apply the distributive property correctly, or a sign error may result.

Chapter 2 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Documents

Transcript of Chapter 2 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.