Download Ch2-Sec 2.1

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2.1 – Slide 1
Chapter 2
Equations, Inequalities, and
Applications
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2.1 – Slide 2
2.1
The Addition Property of
Equality
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2.1 – Slide 3
2.1 The Addition Property of Equality
Objectives
1.
2.
3.
Identify linear equations.
Use the addition property of equality.
Simplify, and then use the addition property of
equality.
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2.1 – Slide 4
2.1 The Addition Property of Equality
Identifying 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, with A ≠ 0.
Some examples of linear and nonlinear equations follow.
4x + 9 = 0,
x2
+ 2x = 5,
2x – 3 = 5,
and
x=7
Linear
1
= 6, and |2x + 6| = 0 Nonlinear
x
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2.1 – Slide 5
2.1 The Addition Property of Equality
Identifying Linear Equations
A solution of an equation is a number that makes the
equation true when it replaces the variable. Equations
that have exactly the same solution sets are equivalent
equations.
A linear equation is solved by using a series of steps
to produce a simpler equivalent equation of the form
x = a number
or
a number = x.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
2.1 – Slide 6
2.1 The Addition Property of Equality
Using the Addition Property of Equality
Addition Property of Equality
If A, B, and C are real numbers, then the equations
A=B
and
A+C=B+C
are equivalent equations.
In words, we can add the same number to each side
of an equation without changing the solution.
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2.1 – Slide 7
2.1 The Addition Property of Equality
Using the Addition Property of Equality
Note
Equations can be thought of in
terms of a balance. Thus, adding
the same quantity to each side
does not affect the balance.
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2.1 – Slide 8
2.1 The Addition Property of Equality
Using the Addition Property of Equality
Example 1 Solve each equation.
Our goal is to get an equivalent equation of the form x = a number.
(a) x – 23 = 8
x – 23 + 23 = 8 + 23
x = 31
Check: 31 – 23 = 8
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(b) y – 2.7 = –4.1
y – 2.7 + 2.7 = –4.1 + 2.7
y = – 1.4
Check: –1.4 – 2.7 = –4.1
2.1 – Slide 9
2.1 The Addition Property of Equality
Using the Addition Property of Equality
The same number may be subtracted from each side of
an equation without changing the solution.
If a is a number and –x = a, then x = –a.
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2.1 – Slide 10
2.1 The Addition Property of Equality
Using the Addition Property of Equality
Example 2 Solve each equation.
Our goal is to get an equivalent equation of the form x = a number.
(a) –12 = z + 5
–12 – 5 = z + 5 – 5
–17 = z
Check: –12 = –17 + 5
(b) 4a + 8 = 3a
4a – 4a + 8 = 3a – 4a
8 = –a
–8 = a
Check: 4(–8) + 8 = 3(–8) ?
–24 = –24
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2.1 – Slide 11
2.1 The Addition Property of Equality
Simplifying and Using the Addition Property of Equality
Check:
5((2 · –36) –3) – (11(–36) + 1) =
Example 3
Solve.
5(2b – 3) – (11b + 1) = 20
10b – 15 – 11b – 1 = 20
–b – 16 = 20
5(–72 –3) – (–396 + 1) =
5(–75) – (–395) =
–375 + 395 = 20
–b – 16 + 16 = 20 + 16
–b = 36
b = –36
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2.1 – Slide 12