Section 2.3 Linear Equations: Clearing Fractions and Decimals 141 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. 1 6 5 10 6 TIP: In Example 1, the fractions can be eliminated by multiplying both sides of the equation by any common multiple of the denominators. For example, try multiplying both sides of the equation by 24: 4 6 8 24 1 a5 6 xb 20x 18 8 20x 26 20x 20 x 13 10 26 20 24 1 a3 4b 24 1 a1 3b 24 a5 6 x 3 4b 24 a1 3b Skill Practice Solve the equation. 2. 2 5 x Answer 2. 45 2 Solving a Linear Equation Containing Fractions Solve the equation. Solution: The LCD of is 30. Multiply by the LCD, 30. Apply the distributive property (recall 30 ). 30 1 30 1 1 6 x 30 1 2 3 30 1 1 5 x 30112 30a1 6 x 2 3b 30a1 5 x 1b 15 x, and 1 1 1 6x, 23 x , 2 3 1 5 x 1 1 6 x 2 3 1 5 x 1 Example 2 1 2 7 4 3 10 x Classroom Example: p. 145, Exercise 22 Avoiding Mistakes Remember to multiply all terms in the equation by the LCD, including those that are not fractions. Clear fractions. Subtract 6x from both sides. Add 20 to both sides. 5x 20 6x 30 5x 6x 20 6x 6x 30 x 20 30 x 20 20 30 20 x 10 x 1 10 1 1 Divide both sides by . x 10 The solution is 10.
miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above