Solutions for Elementary and Intermediate Algebra, 4th edition by Tom Carson

Elementary and Intermediate Algebra, 4th edition




SOLUTIONS
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Elementary and
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Intermediate Algebra,
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4th edition
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Authors:
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Tom Carson, Bill E. Jordan

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, CONTENTS



Chapter 1 Foundations of Algebra..............................................................1
Chapter 2 Solving Linear Equations and Inequalities ..............................14
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Chapter 3 Graphing Linear Equations and Inequalities............................53
Chapter 4 Systems of Linear Equations and Inequalities .........................80
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Chapter 5 Polynomials............................................................................106
Chapter 6 Factoring.................................................................................123
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Chapter 7 Rational Expressions and Equations ......................................142
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Chapter 8 More on Inequalities, Absolute Value, and Functions...........174
Chapter 9 Rational Exponents, Radicals, and Complex Numbers .........182
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Chapter 10 Quadratic Equations and Functions .......................................204
Chapter 11 Exponential and Logarithmic Functions ................................238
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Chapter 12 Conic Sections........................................................................255
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, Chapter 1 32. The number 7.4 is located 0.4 =
4
of the way
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Foundations of Algebra between 7 and 8, so we divide the space between 7
and 8 into 10 equal divisions and place a dot on
the 4th mark to the right of 7.
Exercise Set 1.1
2. {q, r, s, t, u, v, w, x, y, z}
4. {Alaska, Hawaii}
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34. First divide the number line between −7 and −8
6. {2, 4, 6, 8, …} into tenths. The number −7.62 falls between
8. {16, 18, 20, 22, …} −7.6 and −7.7 on the number line. Subdivide this
section into hundredths and place a dot on the 2nd
10. {–2, –1, 0} mark to the left of −7.6 .
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12. Rational because 1 and 4 are integers.
14. Rational because −12 is an integer and all
integers are rational numbers.
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π
16. Irrational because cannot be written as a ratio
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of integers. 36. 6 = 6 because 6 is 6 units from 0 on a number
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8 line.
18. Rational because −0.8 can be expressed as − ,
10 38. −8 = 8 because −8 is 8 units from 0 on a
the ratio of two integers. number line.
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20. Rational because 0.13 can be expressed as the 40. −4.5 = 4.5 because −4.5 is 4.5 units from 0 on a
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fraction , the ratio of two integers. number line.
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3 3 3 3
22. False. There are real numbers that are not rational 42. 2 = 2 because 2 is 2 units from 0 on a
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(irrational numbers). 5 5 5 5
number line.
24. False. There are real numbers that are not natural
44. −67.8 = 67.8 because −67.8 is 67.8 units from 0
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numbers, such as 0, –2, , 0.6 , and π.
4 on a number line.
26. True 46. 2 < 7 because 2 is farther to the left on a number
line than 7.
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28. The number 5 is located of the way between 48. −6 < 5 because −6 is farther to the left on a
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5 and 6, so we divide the space between 5 and 6 number line than 5.
into 2 equal divisions and place a dot on the 1st 50. −19 < −7 because −19 is farther to the left on a
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mark to the right of 5. number line than −7 .
52. 0 > −5 because 0 is farther to the right on a
number line than −5 .
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2 2 54. 2.63 < 3.75 because 2.63 is farther to the left on a
30. The number − is located of the way between
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5 5 number line than 3.75.
0 and −1 , so we divide the space between 0 and 56. −3.5 < −3.1 because −3.5 is farther to the left
−1 into 5 equal divisions and place a dot on the on a number line than −3.1 .
2nd mark to the left of 0.




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