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Chapter 9
Equations,
Inequalities and
Problem Solving
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
9.1
The Addition Property of
Equality
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Linear Equations
An equation is of the form “expression = expression.”
x + 7 = 10
An equation contains an equal sign and an expression
does not.
Equations
7x  6x  4
3(3 y  5)  10 y
Expressions
7x  6x  4
y  1  11 y  21
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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.
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Using the Addition Property to Solve
Equations
Addition Property of Equality
Let a, b, and c represent numbers. Then
a=b
Also,
a=b
and a + c = b + c
and a – c = b – c
are equivalent
equations.
are equivalent
equations.
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Example
Solve x – 4 = 7 for x.
Check:
x47
x4474
x  0  11
x  11
x47
11  4  7
77
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Example
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
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Example
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
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Example
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
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Example
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
Simplify both sides.
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Example
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
Use distributive property.
Simplify left side.
Add 4z to both sides.
Simplify both sides.
Add –6 to both sides.
Simplify both sides.
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