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Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 1 Equations and Inequalities.

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Presentation on theme: "Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 1 Equations and Inequalities."— Presentation transcript:

1 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 1 Equations and Inequalities

2 1 Chapter Outline 1.1Linear Equations, Formulas, and Problem Solving 1.2Linear Inequalities in One Variable 1.3Absolute Value Equations and Inequalities 1.4Complex Numbers 1.5Solving Quadratic Equations 1.6Solving Other Types of Equations 1-2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

3 Learning Objectives In Section 1.1 you will learn how to:  A.Solve linear equations using properties of equality  B.Recognize equations that are contradictions  C.Solve for a specified variable in a formula or literal equation  D.Use the problem-solving guide to solve various problem types 1.1 Linear Equations, Formulas, and Problem Solving 1-3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

4 1-4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

5 1-5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

6 1-6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7 1-7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

8 1-8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

9 1-9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

10 1-10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

11 1-11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

12 1-12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

13 1-13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14 1-14 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

15 1-15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

16 1-16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

17 1-17 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

18 1-18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

19 1-19 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

20 Learning Objectives In Section 1.2 you will learn how to:  A.Solve inequalities and state solutions sets  B.Solve linear inequalities  C.Solve compound inequalities  D.Solve applications of inequalities 1.2 Linear Inequalities in One Variable 1-20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

21 1-21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

22 1-22 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

23 1-23 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

24 1-24 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

25 1-25 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

26 1-26 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

27 1-27 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

28 1-28 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

29 1-29 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

30 1-30 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

31 1-31 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

32 1-32 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

33 1-33 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

34 1-34 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

35 1-35 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

36 Learning Objectives In Section 1.3 you will learn how to:  A.Solve absolute value equations  B.Solve “less than” absolute value inequalities  C.Solve “greater than” absolute value inequalities  D.Solve applications involving absolute value 1.3 Absolute Value Equations and Inequalities 1-36 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

37 1-37 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

38 1-38 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

39 1-39 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

40 1-40 EXAMPLE 2 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

41 1-41 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

42 1-42 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

43 1-43 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

44 1-44 EXAMPLE 4 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

45 1-45 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

46 1-46 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

47 1-47 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

48 1-48 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

49 1-49 EXAMPLE 6 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

50 Learning Objectives In Section 1.4 you will learn how to:  A.Identify and simplify imaginary complex numbers  B.Add and subtract complex numbers  C.Multiply complex numbers and find powers of i  D.Divide complex numbers 1.4 Complex Numbers 1-50 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

51 1-51 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

52 1-52 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

53 1-53 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

54 1-54 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

55 1-55 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

56 1-56 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

57 1-57 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

58 1-58 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

59 1-59 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

60 1-60 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

61 1-61 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

62 1-62 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

63 1-63 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

64 1-64 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

65 Learning Objectives In Section 1.5 you will learn how to:  A.Solve quadratic equations using the zero product property  B.Solve quadratic equations using the square root property of equality  C.Solve quadratic equations by completing the square  D.Solve quadratic equations using the quadratic formula  E.Use the discriminant to identify solutions  F.Solve applications of quadratic equations 1.5 Solving Quadratic Equations 1-65 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

66 1-66 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

67 1-67 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

68 1-68 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

69 1-69 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

70 1-70 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

71 1-71 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

72 1-72 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

73 1-73 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

74 1-74 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

75 1-75 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

76 1-76 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

77 1-77 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

78 1-78 EXAMPLE 6 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

79 1-79 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

80 1-80 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

81 1-81 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

82 1-82 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

83 1-83 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

84 1-84 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

85 1-85 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

86 1-86 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

87 1-87 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

88 Learning Objectives In Section 1.6 you will learn how to:  A.Solve polynomial equations of higher degree  B.Solve rational equations  C.Solve radical equations and equations with rational exponents  D.Solve equations in quadratic form  E.Solve applications of various equation types 1.6 Solving Other Types of Equations 1-88 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

89 1-89 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

90 1-90 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

91 1-91 EXAMPLE 2 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

92 1-92 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

93 1-93 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

94 1-94 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

95 1-95 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

96 1-96 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

97 1-97 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

98 1-98 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

99 1-99 EXAMPLE 6 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

100 1-100 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

101 1-101 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

102 1-102 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

103 1-103 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

104 1-104 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

105 1-105 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

106 1-106 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

107 1-107 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

108 1-108 EXAMPLE 11 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

109 1-109 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

110 1-110 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

111 1-111 EXAMPLE 13 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

112 1-112 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.


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