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Section 1.2 Homework questions? Slide 1 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Section Concepts 1.2 Linear Equations: Clearing Fractions and Decimals Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Solving Linear Equations with Fractions 2.Solving Linear Equations with Decimals

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Section 1.2 Linear Equations: Clearing Fractions and Decimals 1.Solving Linear Equations with Fractions Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sometimes it is simpler to solve an equation with fractions by eliminating the fractions first using a process called clearing fractions. To clear fractions in the equation, we can multiply both sides of the equation by the least common denominator (LCD) of all terms in the equation.

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PROCEDURESolving a Linear Equation in One Variable (continued) Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 Simplify both sides of the equation. Clear parentheses. Consider clearing fractions and decimals (if any are present) by multiplying both sides of the equation by a common denominator of all terms. Combine like terms. Step 2 Use the addition or subtraction property of equality to collect the variable terms on one side of the equation.

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PROCEDURESolving a Linear Equation in One Variable Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 3 Use the addition or subtraction property of equality to collect the constant terms on the other side of the equation. Step 4 Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1. Step 5 Check your answer.

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Example 1Solving a Linear Equation by Clearing Fractions Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Example 2Solving a Linear Equation by Clearing Fractions Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing fractions first.

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Example 3Solving a Linear Equation by Clearing Fractions Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing fractions or clearing parentheses first.

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Example 4Solving a Linear Equation by Clearing Fractions Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing fractions first.

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Example 5You Try Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing fractions first.

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Example 6You Try Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing fractions (or parentheses) first.

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Section 1.2 Linear Equations: Clearing Fractions and Decimals 2.Solving Linear Equations with Decimals Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The same procedure used to clear fractions in an equation can be used to clear decimals. You will first need to identify the decimal fraction.

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Example 7Solving a Linear Equation Containing Decimals Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing decimals. 2.5x + 3 = 1.7x – 6.6

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Example 8Solving a Linear Equation Containing Decimals Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing decimals.

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Example 9You Try Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing decimals. a.1.2w + 3.5 = 2.1 + w b.0.25(x + 2) – 0.15(x + 3) = 4

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Example 9Solving a Linear Equation Containing Decimals Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing decimals. a.1.2w + 3.5 = 2.1 + w

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Example 9Solving a Linear Equation Containing Decimals Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the equation by clearing decimals. b. 0.25(x + 2) – 0.15(x + 3) = 4

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Section Concepts 1.2 Linear Equations: Clearing Fractions and Decimals Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Solving Linear Equations with Fractions 2.Solving Linear Equations with Decimals

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PROCEDURESolving a Linear Equation in One Variable Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 Simplify both sides of the equation. Clear parentheses. Consider clearing fractions and decimals (if any are present) by multiplying both sides of the equation by a common denominator of all terms. Combine like terms. Step 2 Use the addition or subtraction property of equality to collect the variable terms on one side of the equation. Step 3 Use the addition or subtraction property of equality to collect the constant terms on the other side of the equation. Step 4 Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1. Step 5 Check your answer.

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