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Section 1.2 Homework questions?
Slide 1Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Section
Concepts
1.2 Linear Equations: Clearing Fractions and Decimals
Slide 2Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1. Solving Linear Equations with Fractions2. Solving Linear Equations with Decimals
Section 1.2 Linear Equations: Clearing Fractions and Decimals
1. Solving Linear Equations with Fractions
Slide 3Copyright (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.
PROCEDURE Solving a Linear Equation in One Variable
(continued)
Slide 4Copyright (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.
PROCEDURE Solving a Linear Equation in One Variable
Slide 5Copyright (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.
Example 1 Solving a Linear Equation by Clearing Fractions
Slide 6Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Example 2 Solving a Linear Equation by Clearing Fractions
Slide 7Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Solve the equation by clearing fractions first.
1 2 11
6 3 5x x
Example 3 Solving a Linear Equation by Clearing Fractions
Slide 8Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Solve the equation by clearing fractions or clearing parentheses first.
1 1( 7) ( 1) 4
3 2x x
Example 4 Solving a Linear Equation by Clearing Fractions
Slide 9Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Solve the equation by clearing fractions first.
2 42
5 2
x x
Example 5 You Try
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Solve the equation by clearing fractions first.
2 1 7
5 2 10 y
2 1 7 3
5 2 4 10 x x
Example 6 You Try
Slide 11Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Solve the equation by clearing fractions (or parentheses) first.
1 1( 1) ( 3) 2
5 4 z z
1 21
4 6
x x
Section 1.2 Linear Equations: Clearing Fractions and Decimals
2. Solving Linear Equations with Decimals
Slide 12Copyright (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.
Example 7 Solving a Linear Equation Containing Decimals
Slide 13Copyright (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
Example 8 Solving a Linear Equation Containing Decimals
Slide 14Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Solve the equation by clearing decimals.
Example 9 You Try
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Solve the equation by clearing decimals.
a. 1.2w + 3.5 = 2.1 + w
b. 0.25(x + 2) – 0.15(x + 3) = 4
Example 9 Solving a Linear Equation Containing Decimals
Slide 16Copyright (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
Example 9 Solving a Linear Equation Containing Decimals
Slide 17Copyright (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
Section
Concepts
1.2 Linear Equations: Clearing Fractions and Decimals
Slide 18Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1. Solving Linear Equations with Fractions2. Solving Linear Equations with Decimals
PROCEDURE Solving a Linear Equation in One Variable
Slide 19Copyright (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.
