By Margaret L Lial; E John Hornsby; Terry McGinnis
Bankruptcy 1 the true quantity approach 1.1 Fractions research talents: studying Your Math Textbook 1.2 Exponents, Order of Operations, and Inequality examine abilities: Taking Lecture Notes 1.3 Variables, Expressions, and Equations 1.4 actual Numbers and the quantity Line examine talents: Tackling Your Homework 1.5 including and Subtracting actual Numbers examine abilities: utilizing learn playing cards 1.6 Multiplying and Dividing actual Numbers precis routines on Operations with genuine Numbers 1.7 houses of actual Numbers 1.8 Simplifying Expressions learn talents: Reviewing a bankruptcy bankruptcy 2 Linear Equations and Inequalities in a single Variable 2.1 The Addition estate of Equality 2.2 The Multiplication estate of Equality 2.3 extra on fixing Linear Equations precis workouts on fixing Linear Equations learn talents: utilizing learn playing cards Revisited 2.4 An creation to functions of Linear Equations 2.5 formulation and functions from Geometry 2.6 Ratio, share, and percentage 2.7 extra purposes of Linear Equations 2.8 fixing Linear Inequalities learn talents: Taking Math exams bankruptcy three Linear Equations in Variables 3.1 Linear Equations in Variables: the oblong Coordinate approach examine talents: dealing with it slow 3.2 Graphing Linear Equations in Variables 3.3 The Slope of a Line 3.4 Writing and Graphing Equations of traces precis workouts on Linear Equations and Graphs bankruptcy four Exponents and Polynomials 4.1 The Product Rule and gear ideas for Exponents 4.2 Integer Exponents and the Quotient Rule precis routines at the principles for Exponents 4.3 An software of Exponents: medical Notation 4.4 including and Subtracting Polynomials; Graphing easy Polynomials 4.5 Multiplying Polynomials 4.6 designated items 4.7 Dividing Polynomials bankruptcy five Factoring and functions 5.1 the best universal issue; Factoring by way of Grouping 5.2 Factoring Trinomials 5.3 extra on Factoring Trinomials 5.4 targeted Factoring innovations precis workouts on Factoring 5.5 fixing Quadratic Equations by means of Factoring 5.6 functions of Quadratic Equations bankruptcy 6 Rational Expressions and purposes 6.1 the elemental estate of Rational Expressions 6.2 Multiplying and Dividing Rational Expressions 6.3 Least universal Denominators 6.4 including and Subtracting Rational Expressions 6.5 advanced Fractions 6.6 fixing Equations with Rational Expressions precis routines on Rational Expressions and Equations 6.7Applications of Rational Expressions bankruptcy 7 Graphs, Linear Equations, and features 7.1 evaluate of Graphs and Slopes of strains 7.2 assessment of Equations of strains; Linear types precis workouts on Slopes and Equations of strains 7.3 creation to kinfolk and services 7.4 Operations and features of Composition 7.5 edition bankruptcy eight structures of Linear Equations 8.1 fixing structures of Linear Equations through Graphing 8.2 fixing platforms of Linear Equations through Substitution 8.3 fixing structures of Linear Equations through removing precis workouts on fixing platforms of Linear Equations 8.4 platforms of Linear Equations in 3 Variables 8.5 purposes of structures of Linear Equations 8.6 fixing platforms of Linear Equations through Matrix tools bankruptcy nine Inequalities and Absolute worth 9.1 Set Operations and Compound Inequalities 9.2 Absolute price Equations and Inequalities precis workouts on fixing Linear and Absolute price Equations 9.3 Linear Inequalities in Variables bankruptcy 10 Roots, Radicals, and Root capabilities 10.1 Radical Expressions and Graphs 10.2 Rational Exponents 10.3 Simplifying Radical Expressions 10.4 including and Subtracting Radical Expressions 10.5 Multiplying and Dividing Radical Expressions precis routines on Operations with Radicals and Rational Exponents 10.6 fixing Equations with Radicals 10.7 complicated Numbers bankruptcy eleven Quadratic Equations, Inequalities, and capabilities 11.1 fixing Quadratic Equations via the sq. Root estate 11.2 fixing Quadratic Equations via finishing the sq. 11.3 fixing Quadratic Equations via the Quadratic formulation 11.4 Equations Quadratic in shape precis routines on fixing Quadratic Equations 11.5 formulation and additional functions 11.6 Graphs of Quadratic services 11.7 extra approximately Parabolas and Their purposes 11.8 Polynomial and Rational Inequalities bankruptcy 12 Inverse, Exponential, and Logarithmic features 12.1 Inverse services 12.2 Exponential features 12.3 Logarithmic features 12.4 homes of Logarithms 12.5 universal and normal Logarithms 12.6 Exponential and Logarithmic Equations; additional functions bankruptcy thirteen Nonlinear capabilities, Conic Sections, and Nonlinear platforms 13.1 extra Graphs of features 13.2 The Circle and the Ellipse 13.3 The Hyperbola and capabilities outlined via Radicals 13.4 Nonlinear platforms of Equations 13.5 Second-Degree Inequalities and structures of Inequalities bankruptcy 14 Sequences and sequence 14.1 Sequences and sequence 14.2 mathematics Sequences 14.3 Geometric Sequences 14.4 The Binomial Theorem Appendices A units B evaluate of Exponents, Polynomials, and Factoring C man made department D An advent to Calculators
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The product of a number and 3 is 6. 73. Three times a number is equal to 8 more than twice the number. 74. Twelve divided by a number equals 13 times that number. Identify each as an expression or an equation. See Example 6. 75. 3x + 21x - 42 76. 8y - 13y + 52 77. 7t + 21t + 12 = 4 78. 9r + 31r - 42 = 2 79. x + y = 9 80. x + y - 9 A mathematical model is an equation that describes the relationship between two quantities. 212x - 347, where x is a year between 1943 and 2005 and y is age in years.
51x - 42 = 80; 20 7 1 x + = 4; 5 10 2 66. 21x - 52 = 70; 40 Write each word statement as an equation. Use x as the variable. Find all solutions from the set 52, 4, 6, 8, 106. See Example 5. 67. The sum of a number and 8 is 18. 68. A number minus three equals 1. 69. Sixteen minus three-fourths of a number is 13. 70. The sum of six-fifths of a number and 2 is 14. 71. One more than twice a number is 5. 72. The product of a number and 3 is 6. 73. Three times a number is equal to 8 more than twice the number.
6 - 3 | 4 ` 5 51. ” Is this true? Explain. 52. Concept Check True or false: If a is negative, then | a | = - a. Select the lesser of the two given numbers. See Examples 3 and 4. 53. - 11, - 3 54. - 8, - 13 55. - 7, - 6 56. - 16, - 17 57. 4, | - 5 | 58. 4, | - 3 | 59. 5 | 60. 8 | 61. - | - 6 |, - | - 4 | 62. - | - 2 |, - | - 3 | 63. | 5 - 3 |, | 6 - 2 | 64. | 7 - 2 |, | 8 - 1 | Decide whether each statement is true or false. See Examples 3 and 4. 66. - 8 7 - 2 67. - 4 … - 1 - 52 69. | - 6 | 6 | - 9 | 70.