Copyright © 2012, 2008, 2004 Pearson Education, Inc. Mrs. Rivas International Studies Charter School. Bell Ringer

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

Mrs. Rivas

International Studies Charter

School.

Bell RingerEvaluate if and .

a)

b)

c)

d)

Chapter 2 Section 1

Objectives

1


The Addition Property of Equality

Identify linear equations.

Use the addition property of equality.

Simplify, then use the addition property of equality.

2.1

2

3


An equation is a statement asserting that two algebraic expressions are equal.

Slide 2.1-3

Definitions.

Equation5 2x 5x

Remember that an equation (to solve) includes an equals symbol which distinguishes is from an expression (to simplify or evaluate).

Expression

A solution of an equation is a number that makes the equation true when it replaces the variable.

An equation is solved by finding it solution set, the set of all solutions.

Equations with exactly the same solution sets are equivalent equations.


Objective 1


Slide 2.1-4


Linear Equation in One VariableA linear equation in one variable can be written in the form

where A, B, and C are real numbers, and with A ≠ 0.

,Ax B C

2 2 5,x x 1

6,x

2 6 0x

4 9 0,x 2 3 5,x 7x Linear Equations

Nonlinear Equations

Slide 2.1-5


The simplest type of equation is a linear equation.


Objective 2


Slide 2.1-6


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

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.

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.

Slide 2.1-7



Solution:

12 3x

122 3 121x 9x

9The solution set is .

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

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.

Slide 2.1-8

EXAMPLE 1 Applying the Addition Property of Equality


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.

Slide 2.1-9



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

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.

Slide 2.1-10

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


Solution:

Solve.

22 16x

22 116 166x

38 x

22 16x

Check:

3822 16

22 22

The solution set is .{ 38}

Slide 2.1-11



Solution:

Solve.

7 91

2 2p p

1 p

7 91

2 2p p

Check:

7 2 9

2 2 21 1

9 9

2 2

The solution set is .{1}

7 91

7

22

7

22pp pp

Slide 2.1-12

EXAMPLE 4 Subtracting a Variable Expression


Solution:

0 9 21 22x x xx

10 9x

The solution set is .{ 1}

10 2 9x x

Check:

110 91 2 10 1 2 9

Solve.

Slide 2.1-13

EXAMPLE 5 Applying the Addition Property of Equality Twice

1x 11 11


Objective 3

Simplify, and then use the addition property of equality.

Slide 2.1-14


Solution:

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

Slide 2.1-15

EXAMPLE 6 Combining Like Terms When Solving


Solution:

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.

Slide 2.1-16

EXAMPLE 7 Using the Distributive Property When Solving

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Mrs. Rivas International Studies Charter School. Bell Ringer