Chapter 9 - XYZ Custom Plus

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Chapter Pretest The pretest below contains problems that are representative of the problems you will find in the chapter. Simplify. 1. 4a 2 1 2 5a 1 8 2. 2(5y 2 6) 1 4y Solve each equation. 3. a 1 4 5 22 4. 5y 1 9 2 4y 5 27 1 11 5. 1 } 5 x 5 3 6. 22x 1 9 5 11 7. 2a 1 1 5 5(a 2 2) 2 1 8. x } 3 2 x } 4 5 5 9. Find the value of 3x 2 4 when x 5 22. 10. Is x 5 5 a solution to the equation 6x 2 28 5 1? 11. The sum of a number and 6 is 217. Find the number. 12. If four times a number is decreased by 7, the result is 25. Find the number. 13. Plot the following points: (3, 1), (23, 0), (2, 21), (22, 22). −5−4−3−2−1 −1 −2 −3 −4 −5 y 5 4 3 2 1 1 2 3 4 5 x 14. Graph y 5 3x 2 1. −5−4−3−2−1 −1 −2 −3 −4 −5 y 5 4 3 2 1 1 2 3 4 5 x Getting Ready for Chapter 9 The problems below review material covered previously that you need to know in order to be successful in Chapter 9. If you have any difficulty with the problems here, you need to go back and review before going on to Chapter 9. Simplify. 1. 22 1 7 2. 180 2 45 3. 22 1 (24) 4. 5 } 8 1 3 } 4 5. (24)(5) 6. 6 } 23 7. 3 } 2 (12) 8. 1 2 5 } 4 21 2 4 } 5 2 9. 1 2 5 } 4 21 8 } 15 2 10. 24(21) 1 9 11. 1 } 3 (15) 1 2 12. 5 } 9 (95 2 32) 13. 3x 1 7x 14. 24(3x ) 15. 4(x 2 5) 16. 2 1 1 }2 x 2 17. Write in symbols: the sum of x and 2. 18. Find the perimeter. 3x x 510 Chapter 9 Solving Equations and Inequalities
The Distributive Property and Algebraic Expressions We recall that the distributive property from Section 1.5 can be used to find the area of a rectangle using two different methods. x 3 4 x 3 Area 5 4(x ) 1 4(3) Area 5 4(x 1 3) 5 4x 1 12 5 4x 1 12 Since the areas are equal, the equation 4(x 1 3) 5 4(x ) 1 4(3) is a true statement. 4 9.1 Objectives A Apply the distributive property to an expression. B Combine similar terms. C Find the value of an algebraic expression. D Solve applications involving complementary and supplementary angles. Examples now playing at MathTV.com/books A The Distributive Property Example 1 Apply the distributive property to the expression: 5(x 1 3) Practice Problems 1. Apply the distributive property to the expression 6(x 1 4). Solution Distributing the 5 over x and 3, we have 5(x 1 3) 5 5(x) 1 5(3) Distributive property 5 5x 1 15 Multiplication Remember, 5x means “5 times x.” The distributive property can be applied to more complicated expressions involving negative numbers. Example 2 Multiply: 24(3x 1 5) 2. Multiply: 23(2x 1 4) Solution Multiplying both the 3x and the 5 by 24, we have 24(3x 1 5) 5 24(3x) 1 (24)5 Distributive property 5 212x 1 (220) Multiplication 5 212x 2 20 Definition of subtraction Notice, first of all, that when we apply the distributive property here, we multiply through by 24. It is important to include the sign with the number when we use the distributive property. Second, when we multiply 24 and 3x, the result is 212x because 24(3x) 5 (24 ? 3)x Associative property 5 212x Multiplication Answers 1. 6x 1 24 2. 26x 2 12 9.1 The Distributive Property and Algebraic Expressions 511
Page 1: Solving Equations and Inequalities
Page 5 and 6: 9.1 The Distributive Property and A
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Page 9 and 10: 9.1 Problem Set 517 Problem Set 9.1
Page 11 and 12: 9.1 Problem Set 519 Find the value
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Page 15 and 16: Introduction . . . The Addition Pro
Page 17 and 18: 9.2 The Addition Property of Equali
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Page 23 and 24: The Multiplication Property of Equa
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Page 31 and 32: Introduction . . . Linear Equations
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9.6 Evaluating Formulas 561 The rat
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9.6 Problem Set 563 Problem Set 9.6
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9.6 Problem Set 565 B Maximum Heart
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9.6 Problem Set 567 Applying the Co
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Chapter 9 Summary Combining Similar
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Chapter 9 Review Simplify the expre
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Chapter 9 Cumulative Review 573 28.
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Chapter 9 Projects Solving Equation
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Chapter 9 - XYZ Custom Plus

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