19 22 Solving Equations by Multiplying and Dividing Objectives 221 Use the

19 22 solving equations by multiplying and dividing

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2.2: Solving Equations by Multiplying and Dividing Objectives: 2.2.1: Use the multiplication property to solve equations 2.2.2: Use the multiplication property to solve an application 20
The Multiplication Property of Equality Suppose we want to solve this equation: 6x = 18. The addition property doesn’t help to solve the equation. 21
2.2.1: Solving Equations by Using the Multiplication Property Examples: Solve the following equations 1. 6x = 18 2. 5x = 35 3. 9x = 54 4. = 6 5. = 9 3 x 5 x 22
2.2.1: Solving Equations by Using the Multiplication Property Examples: Solve the following equations Solving Equations by Using Reciprocals 1. x = 9 2. x = 18 Solving Equations by Combining Like Terms 1. 3x + 5x = 40 2. 7x + 4x = 66 5 3 3 2 23
2.2.2: Use the Multiplication Property to Solve an Application Example: On her first day on the job in a photography lab, Nancy processed all of the film given to her. The following day, her boss gave her four times as much film to process. Over the two days, she processed 60 rolls of film. How many rolls did she process on the first day? 24
2.3: Combining the Rules to Solve Equations Objectives: 2.3.1: Use both addition and multiplication to solve equations 2.3.2: Solve equations involving fractions 2.3.3: Solve applications 25
2.3.1: Use Both Addition and Multiplication to Solve Equations Examples: Solve the following equations 1. 3x 5 = 4 2. 4x 7 = 17 3. 5x 11 = 2x 7 4. 7x 12 = 2x 9 26
2.3.1: Use Both Addition and Multiplication to Solve Equations Examples: Solve the following equations Applying the Properties of Equality with Like Terms 1. 8x + 2 3x = 8 + 3x + 2 2. 7x 3 5x = 10 + 4x + 3 Applying the Properties of Equality with Parentheses 1. x + 3(3x 1) = 4(x + 2) + 4 2. x + 5(x + 2) = 3(3x 2) + 18 27
2.3.2: Solve Equations Involving Fractions To solve an equation involving fractions, the first step is to multiply both sides of the equation by the least common multiple (LCM) of all denominators in the equation. This clears the equation of fractions, and we can proceed as before. The LCM of a set of denominators is also called the least common denominator (LCD). Examples: Solve the following equations 1. = 2. + 1 = 2 x 3 2 6 5 5 1 2 x 2 x 28
Conditional Equations, Identities, and Contradictions An equation that is true for only particular values of the variable is called a conditional equation . Here the equation can be written in the form ax + b = 0 in which a ≠ 0 An equation that is true for all possible values of the variable is called an identity . In this case, both a and b are 0, so we get the equation 0 = 0. This is the case, if both sides of the equation reduce to the same expression (a true statement). An equation that is never true , no matter what the value of the variable, is called a contradiction . For example, if a is 0 but b is 4, a contradiction results. This is the case if the equation simplifies as a false statement 29
Identities and Contradictions Examples: Solve the following equations Solving Identity Equation 1.

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