140 Chapter 2 Linear Equations and Inequalities Section 2.3 Linear Equations: Clearing Fractions and Decimals 1. Solving Linear Equations Containing Fractions Linear equations that contain fractions can be solved in different ways. The first procedure, illustrated here, uses the method outlined in Section 2.2. To isolate the variable term, add to both sides. Find the common denominator on the right-hand side. Simplify. Multiply by the reciprocal of which is The solution is 6 1 5 a13 12 13 10 5 6 6 5 a5 6 5 6 5 6 xb Sometimes it is simpler to solve an equation with fractions by eliminating the 5 6 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. In this case, the LCD of and is 12. Because each denominator in the equation is a factor of 12, we can simplify common factors to leave integer coefficients for each term. 13 56 x, 34 , 56 x 34 13 , 13 10 x . 6 5 . 5 6 , 2 b x 13 12 x 4 12 9 12 3 4 x 3 4 3 4 1 3 3 4 x 3 4 1 3 Concepts 1. Solving Linear Equations Containing Fractions 2. Solving Linear Equations Containing Decimals Solving a Linear Equation by Clearing Fractions Solve the equation by clearing fractions first. Solution: , 56 The LCD of and is 12. Multiply both sides of the equation by the LCD, 12. 5 6 Apply the distributive property (recall that 1 2. Simplify common factors to clear the fractions. Add 9 to both sides. Divide both sides by 10. The solution is 13 215x2 3132 4112 10x 9 4 10x 9 9 4 9 10x 13 13 10 10x 10 x 10. 13 10 12 12 12 1 a5 6 xb 12 1 a3 4b 12 1 a1 3b 12 a5 6 x 3 4b 12 a1 3b 13 34 x , 3 4 1 3 5 6 x 3 4 1 3 Example 1 Skill Practice Solve the equation by clearing fractions. 1. 2 5 y 1 2 7 10 Classroom Example: p. 145, Exercise 18 TIP: Recall that the multiplication property of equality indicates that multiplying both sides of an equation by a nonzero constant results in an equivalent equation. 2 3 4 Answer 1. 3
miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above