142 Chapter 2 Linear Equations and Inequalities Skill Practice Solve the equation. 3. 1 5 1z 12 Skill Practice Solve the equation. 4. x 1 4 Answers 3. 4. 1 7 3 Solving a Linear Equation Containing Fractions Solve the equation. Solution: Clear parentheses. The LCD of Apply the distributive property. Combine like terms. Subtract 11. 1 31x 72 1 21x 12 4 2x 14 3x 3 24 x 11 24 x 11 11 24 11 x 13 x 1 13 1 Divide by 1. The solution is 13. Solving a Linear Equation Containing Fractions Solve. Solution: The LCD of and is 10. Multiply both sides by 10. Apply the distributive property. Clear fractions. Apply the distributive property. Simplify both sides of the equation. Subtract 16 from both sides. Divide both sides by 4 3 The solution is . 5 21x 22 51x 42 20 2x 4 5x 20 20 3x 16 20 3x 16 16 20 16 3x 4 x 4 3 3. 3x 3 4 3 2 10 1 ax 2 5 b 10 1 ax 4 2 b 10 1 a2 1b 10 ax 2 5 x 4 2 b 10 a2 1b 21 x 2 5 , x 4 2 , x 2 5 x 4 2 2 1 x 2 5 x 4 2 2 Example 4 x 13 6 1 1 3 x 6 1 7 3 6 1 a 1 2 xb 6 1 a 1 2b 6142 13 x, 73 , 12 x, 12 , and 41 is 6. 6 a1 3 x 7 3 1 2 x 1 2b 6142 1 3 x 7 3 1 2 x 1 2 4 1 31x 72 1 21x 12 4 Example 3 2 2 3 3 1 4 1z 32 2 Classroom Example: p. 145, Exercise 26 TIP: In Example 3 both parentheses and fractions are present within the equation. In such a case, we recommend that you clear parentheses first. Then clear the fractions. x 2 6 1 Classroom Example: p. 145, Exercise 32 Avoiding Mistakes In Example 4, several of the fractions in the equation have two terms in the numerator. It is important to enclose these fractions in parentheses when clearing fractions. In this way, we will remember to use the distributive property to multiply the factors shown in blue with both terms from the numerator of the fractions.
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