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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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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.
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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.
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1-4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-14 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-17 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-19 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-22 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-23 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-24 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-25 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-26 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-27 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-28 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-29 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-30 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-31 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-32 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-33 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-34 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-35 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-37 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-38 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-39 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-40 EXAMPLE 2 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-41 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-42 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-43 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-44 EXAMPLE 4 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-45 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-46 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-47 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-48 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-49 EXAMPLE 6 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-51 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-52 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-53 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-54 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-55 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-56 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-57 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-58 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-59 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-60 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-61 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-62 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-63 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-64 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-66 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-67 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-68 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-69 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-70 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-71 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-72 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-73 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-74 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-75 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-76 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-77 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-78 EXAMPLE 6 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-79 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-80 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-81 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-82 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-83 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-84 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-85 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-86 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-87 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-89 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-90 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-91 EXAMPLE 2 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-92 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-93 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-94 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-95 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-96 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-97 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-98 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-99 EXAMPLE 6 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-100 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-101 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-102 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-103 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-104 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-105 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-107 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-108 EXAMPLE 11 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-111 EXAMPLE 13 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-112 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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