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Chapter 2
Equations,
Inequalities and
Problem Solving
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Bellwork:
1. Recall that the perimeter of 2. Given the following triangle,
a figure is the total distance
express it perimeter as an
around the figure. Given the
algebraic containing the
following rectangle, express
variable x.
the perimeter as an algebraic
expression containing the
variable x.
5 cm
(3x – 1) cm
5x ft
(4x – 1) ft
(2x + 5) cm
5x ft
(4x – 1) ft
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2
Bellwork:
1. Recall that the perimeter of 2. Given the following triangle,
a figure is the total distance
express it perimeter as an
around the figure. Given the
algebraic containing the
following rectangle, express
variable x.
the perimeter as an algebraic
expression containing the
variable x.
5 cm
(3x – 1) cm
5x ft
(4x – 1) ft
(18x – 2) ft
5x ft
(2x + 5) cm
(4x – 1) ft
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
3
Bellwork:
1. Recall that the perimeter of 2. Given the following triangle,
a figure is the total distance
express it perimeter as an
around the figure. Given the
algebraic containing the
following rectangle, express
variable x.
the perimeter as an algebraic
expression containing the
variable x.
5 cm
(3x – 1) cm
5x ft
(5x + 9) cm
(4x – 1) ft
(18x – 2) ft
5x ft
(2x + 5) cm
(4x – 1) ft
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
4
2.2
The Addition Property of
Equality
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Objectives:
Use
the addition property of
equality to solve linear equations
Simplify
an equation and then use
the addition property of equality
Write
word phrases as algebraic
expressions
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
6
Linear Equations
An equation is of the form “expression = expression.”
(Ex.) x + 7 = 10
An equation contains an equal sign and
an expression does not.
Equations
7x  6x  4
3(3 y  5)  10 y
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Expressions
7x  6x  4
y  1  11 y  21
7
Linear Equations
An equation is of the form “expression = expression.”
(Ex.) x + 7 = 10
An equation
contains an equal sign and
an expression
does not.
Equations
7x  6x  4
3(3 y  5)  10 y
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Expressions
7x  6x  4
y  1  11 y  21
8
Linear Equations
Linear Equation in One Variable
A linear equation in one variable can be written in
the form
Ax + B = C
where A, B, and C are real numbers and A ≠ 0.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
9
Linear Equations
Linear Equation in One Variable
A linear equation in one variable can be written in
the form
Ax + B = C
Standard Form
where A, B, and C are real numbers and A ≠ 0.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
10
Addition Property of Equality
Let a, b, and c represent numbers. Then,
a=b
a=b
and a + c = b + c
and a – c = b – c
are equivalent
equations.
are equivalent
equations.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
11
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
12
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
13
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
14
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
15
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
16
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
17
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
18
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
19
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
20
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Check:
x47
11  4  7
77
21
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Check:
x47
11  4  7
77
True Statement!
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
22
Example 1
Solve x – 4 = 7 for x.
x47
x4474
x  0  11
x  11
Check:
x47
11  4  7
77
True Statement!
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
23
Example 2
Solve: y – 1.2 = –3.2 – 6.6
y  1.2  3.2  6.6
y  1.2  9.8
y  1.2  1.2  9.8  1.2
y  8.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
24
Example 2
Solve: y – 1.2 = –3.2 – 6.6
y  1.2  3.2  6.6
y  1.2  9.8
y  1.2  1.2  9.8  1.2
y  8.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
25
Example 2
Solve: y – 1.2 = –3.2 – 6.6
y  1.2  3.2  6.6
y  1.2  9.8
y  1.2  1.2  9.8  1.2
y  8.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
26
Example 2
Solve: y – 1.2 = –3.2 – 6.6
y  1.2  3.2  6.6
y  1.2  9.8
y  1.2  1.2  9.8  1.2
y  8.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
27
Example 2
Solve: y – 1.2 = –3.2 – 6.6
y  1.2  3.2  6.6
y  1.2  9.8
y  1.2  1.2  9.8  1.2
y  8.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
28
Example 2
Solve: y – 1.2 = –3.2 – 6.6
y  1.2  3.2  6.6
y  1.2  9.8
y  1.2  1.2  9.8  1.2
y  8.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
29
Example 3
Solve: 6x + 8 – 5x = 8 – 3
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
30
Example 3
Solve: 6x + 8 – 5x = 8 – 3
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
31
Example 3
Solve: 6x + 8 – 5x = 8 – 3
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
32
Example 3
Solve: 6x + 8 – 5x = 8 – 3
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
33
Example 3
Solve: 6x + 8 – 5x = 8 – 3
–
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
34
Example 3
Solve: 6x + 8 – 5x = 8 – 3
–
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
35
Example 3
Solve: 6x + 8 – 5x = 8 – 3
–
6 x  8  5x  8  3
6 x  5x  8  8  3
x 8  5
x 88  58
x  3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
36
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
37
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
38
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
39
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
40
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
41
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
42
Example 4
Solve: 3(3x – 5) = 10x
3(3x  5)  10 x
3(3x )  3(5)  10 x
9 x  15  10 x
9 x  15  9 x  10 x  9 x
15  x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
43
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
44
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
45
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
46
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
47
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
48
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
49
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
50
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
51
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
52
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
53
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
54
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
55
Example 5
Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – 18
3p + (– 2p) – 11 = 2p + (– 2p) – 18
Simplify both sides.
Add –2p to both sides.
p – 11 = –18
Simplify both sides.
p – 11 + 11 = –18 + 11
Add 11 to both sides.
p = –7
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Simplify both sides.
56
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
57
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
58
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
59
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
60
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
61
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
62
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
63
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
64
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
65
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
66
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
67
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
68
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
69
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
70
Example 6
Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
6 – 3z + 4z = – 4z + 4z
6+z=0
6 + (–6) + z = 0 + (–6)
z = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
71
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m – 60) feet long.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
72
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m – 60) feet long.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
73
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m – 60) feet long.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
74
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m – 60) feet long.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
75
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m – 60) feet long.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
76
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m – 60) feet long.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
77
Example 7
The Verrazano-Narrows Bridge in New York City is the
longest suspension bridge in North America. The Golden
Gate Bridge in San Francisco is 60 feet shorter than the
Verrazano-Narrows Bridge. If the length of the VerrazanoNarrows Bridge is m feet, express the length of the Golden
Gate Bridge as an algebraic expression in m.
The Golden Gate Bridge is 60 feet shorter.
We have that its length is:
Length of Verrazano Bridge minus 60
m
‒
60
The Golden Gate Bridge is (m
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
– 60) feet long.
78
Closure:
1.
What is standard form?
2.
What is the difference between an
expression and an equation?
3.
What is the Addition Property of
Equality?
4.
What should you do to both sides of an
equation?
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
79