122 Chapter 2 Linear Equations and Inequalities Answer 1. 536 TIP: The fractions in this equation can be eliminated by multiplying both sides of the equation by any common multiple of the denominators. These include 12, 24, 36, 48, and so on. We chose 12 because it is the least common multiple. Skill Practice Solve the equation by clearing fractions. 1. 2 5 y 1 2 7 10 In this section, we combine the process for clearing fractions and decimals with the general strategies for solving linear equations. To solve a linear equation, it is important to follow these steps. Solving a Linear Equation in One Variable 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. Solving a Linear Equation Containing Fractions Solve the equation. Solution: The LCD of , and is 30. Multiply by the LCD, 30. Apply the distributive property (recall ). Clear fractions. Subtract 6x from both sides. 1 6 5x 20 6x 30 5x 6x 20 6x 6x 30 x 20 30 30 30 1 30 1 1 6 x 30 1 2 3 30 1 1 5 x 30112 30 a 1 6 x 2 3 b 30 a 1 5 x 1b 1 1 x, 5x 1 16 23 x , 2 3 1 5 x 1 1 6 x 2 3 1 5 x 1 Example 2 5 10 6
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