Chapter 9 - XYZ Custom Plus

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568 Chapter 9 Solving Equations and Inequalities Maintaining Your Skills Simplify. 77. 81. } 3 5 } } } 4 5 } 78. } 1 2 } 1 }1 4 } } } 1 82. 4 } 1 }1 8 } } 5 7 } } } 6 7 } 79. } 1 2 } 2 }1 4 } } } 1 83. 4 } 2 }1 8 } 1 1 } 1 2 } } 1 2 } 1 2 } 80. } 3 5 } 1 }3 7 } } } 3 84. 5 } 2 }3 7 } 1 1 } 1 3 } } 1 2 } 1 3 } } 5 7 } 1 }5 8 } } } 5 7 } 2 }5 8 }
Chapter 9 Summary Combining Similar Terms [9.1] Two terms are similar terms if they have the same variable part. The expressions 7x and 2x are similar because the variable part in each is the same. Similar terms are combined by using the distributive property. Examples 1. 7x 1 2x 5 (7 1 2)x 5 9x Finding the Value of an Algebraic Expression [9.1] An algebraic expression is a mathematical expression that contains numbers and variables. Expressions that contain a variable will take on different values depending on the value of the variable. 2. When x 5 5, the expression 2x 1 7 becomes 2(5) 1 7 5 10 1 7 5 17 The Solution to an Equation [9.2] A solution to an equation is a number that, when used in place of the variable, makes the equation a true statement. The Addition Property of Equality [9.2] Let A, B, and C represent algebraic expressions. If A 5 B then A 1 C 5 B 1 C In words: Adding the same quantity to both sides of an equation will not change the solution. 3. We solve x 2 4 5 9 by adding 4 to each side. x 2 4 5 9 x 2 4 1 4 5 9 1 4 x 1 0 5 13 x 5 13 The Multiplication Property of Equality [9.3] Let A, B, and C represent algebraic expressions, with C not equal to 0. If A 5 B then AC 5 BC In words: Multiplying both sides of an equation by the same nonzero number will not change the solution to the equation. This property holds for division as well. 4. Solve } 1 }x 5 5. 3 } 1 3 }x 5 5 3 ? } 1 3 }x 5 3 ? 5 x 5 15 Steps Used to Solve a Linear Equation in One Variable [9.4] Step 1 Simplify each side of the equation. Step 2 Use the addition property of equality to get all variable terms on one side and all constant terms on the other side. 5. 2(x 2 4) 1 5 5 211 2x 2 8 1 5 5 211 2x 2 3 5 211 2x 2 3 1 3 5 211 1 3 2x 5 28 } 2 x } 5 } 2 8 } 2 2 Chapter 9 Summary x 5 24 569
Page 1 and 2:
Solving Equations and Inequalities
Page 3 and 4:
The Distributive Property and Algeb
Page 5 and 6:
9.1 The Distributive Property and A
Page 7 and 8:
9.1 The Distributive Property and A
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
Page 13 and 14: 9.1 Problem Set 521 91. Temperature
Page 15 and 16: Introduction . . . The Addition Pro
Page 17 and 18: 9.2 The Addition Property of Equali
Page 21 and 22: 9.2 Problem Set 529 Applying the Co
Page 23 and 24: The Multiplication Property of Equa
Page 25 and 26: 9.3 The Multiplication Property of
Page 29 and 30: 9.3 Problem Set 537 Find the value
Page 31 and 32: Introduction . . . Linear Equations
Page 33 and 34: 9.4 Linear Equations in One Variabl
Page 37 and 38: 9.4 Problem Set 545 C Applying the
Page 39 and 40: Introduction . . . Applications As
Page 41 and 42: 9.5 Applications 549 Step 2 Assign
Page 43 and 44: 9.5 Applications 551 Example 4 The
Page 45 and 46: 9.5 Applications 553 Step 2 Assign
Page 49 and 50: 9.5 Problem Set 557 Coin Problems 3
Page 51 and 52: Introduction . . . Evaluating Formu
Page 53 and 54: 9.6 Evaluating Formulas 561 The rat
Page 57 and 58: 9.6 Problem Set 565 B Maximum Heart
Page 59: 9.6 Problem Set 567 Applying the Co
Page 63 and 64: Chapter 9 Review Simplify the expre
Page 65 and 66: Chapter 9 Cumulative Review 573 28.
Page 67 and 68: Chapter 9 Projects Solving Equation
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