78 CHAPTER 1 The Real Number System
Values of a variable that make an equation true are
solutions of the equation.
Is 2 a solution of
Let
False
2 is not a solution.13 = 18
5122 + 3 18 x=2.5 x+ 3 =18?CONCEPTS EXAMPLES
1.4 Real Numbers and the Number Line
Ordering Real Numbers
ais less than bifais to the left of bon the number line.
The additive inverse of xis
The absolute value of x, written is the distance between
xand 0 on the number line.
|x|,- x.
Graph 0, and 3.| 13 |= 13 | 0 |= 0 |- 5 |= 5
- 152 =- 5 - 1 - 72 = 7 - 0 = 0
- 263 370 063
- 2,
–3–2–1012341.5 Adding and Subtracting Real Numbers
Adding Two Signed Numbers
Same sign Add their absolute values. The sum has that
same sign.
Different signs Subtract their absolute values. The sum
has the sign of the number with greater absolute value.
Definition of Subtraction
xyx 1 y 2Add.Subtract.13 - 1 - 82 = 13 + 8 = 21
- 2 - 1 - 62 =- 2 + 6 = 4
- 3 - 4 =- 3 + 1 - 42 =- 7
- 5 + 13 = 8
7 + 1 - 122 =- 5
- 8 + 1 - 52 =- 13
9 + 4 = 13
1.6 Multiplying and Dividing Real
Numbers
Multiplying and Dividing Two Signed Numbers
Same sign The product (or quotient) is positive.
Different signs The product (or quotient) is negative.
Multiply or divide.- 18
9
=- 2
49
- 7
=- 7
- 24
- 6
= 4 - 6152 =-30 6 1 - 52 =- 30
6 # 5 = 30 - 71 - 82 = 56
20
4
= 5
Definition of Division
0 divided by a nonzero number equals 0.
Division by 0 is undefined.
x
yx#
1
y, yZ 0is undefined.5
0
0
5
= 0
10
2
= 10 #
1
2
= 5
1.7 Properties of Real Numbers
Commutative Properties
Associative Properties
Identity Properties
a# 1 a 1 #aa
a 0 a 0 aa1 ab 2 ca 1 bc 21 ab 2 ca 1 bc 2abbaabba9 # 1 =9 1# 9 = 9
- 7 + 0 =-7 0+ 1 - 72 =- 7
3 - 216244 =- 2316244
13 + 42 + 8 = 3 + 14 + 82
51 - 32 = 1 - 325
7 + 1 - 12 =- 1 + 7
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