Section 2.3 Linear Equations: Clearing Fractions and Decimals 121 Linear Equations: Clearing Fractions and Decimals Section 2.3 1. 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 set is e 13 10 4 12 13 12 6 1 5 a 13 10 5 6 5 6 x x xb 13 12 2 9 12 b x f . 6 5 . 5 6 5 6 6 5 a 5 6 , 3 4 5 6 x 3 4 3 4 1 3 3 4 x 3 4 1 3 Sometimes it is simpler to solve an equation with fractions by eliminating the fractions first by using a process called clearing fractions.To clear fractions in the equation we can apply the multiplication property of equality to multiply both sides of the equation by the least common denominator (LCD). 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. Solving a Linear Equation by Clearing Fractions Solve the equation by clearing fractions first. Solution: The LCD of and is 12. Multiply both sides of the equation by the LCD, 12. 5 6 Apply the distributive property (recall that 12 12 1 2. Simplify common factors to clear the fractions. Add 9 to both sides. Divide both sides by 10. The solution set is e 13 10 215x2 3132 4112 10x 9 4 10x 9 9 4 9 10x 13 13 10 10x 10 x f . 13 10 12 1 a 5 6 xb 12 1 a 3 4 b 12 1 a 1 3 b 12 a 5 6 x 3 4 b 12 a 1 3 b 1 3 5 6 x, 3 4 x , 3 4 1 3 5 6 x 3 4 1 3 Example 1 13 5 6x, 34 , 56 x 34 13 , 2 3 4 Concepts 1. Linear Equations Containing Fractions 2. Linear Equations Containing Decimals 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.
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