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2-7 Solving Equations with Rational Numbers Learn to solve equations with rational numbers. 2-7 Solving Equations with Rational Numbers Additional Examples 1A: Solving Equations with Decimals Solve. m + 4.6 = 9 m + 4.6 = 9 – 4.6 = – 4.6 m = 4.4 Use the Subtraction Property of Equality. Subtract 4.6 from both sides. Remember! Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation. 2-7 Solving Equations with Rational Numbers Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 8.2p = –32.8 8.2 8.2 p = –4 Use the Division Property of Equality. Divide both sides by 8.2 2-7 Solving Equations with Rational Numbers Additional Examples 1C: Solving Equations with Decimals Solve. x = 15 1.2 x = 1.2 • 15 1.2 • 1.2 x = 18 Use the Multiplication Property of Equality. Multiply both sides by 1.2 2-7 Solving Equations with Rational Numbers Check It Out: Example 1A & 1B Solve. A. m + 9.1 = 3 m + 9.1 = 3 –9.1 = –9.1 m = –6.1 Use the Subtraction Property of Equality. Subtract 9.1 from both sides. B. 5.5b = 75.9 75.9 5.5 b = 5.5 5.5 b = 13.8 Use the Division Property of Equality. Divide both sides by 5.5 2-7 Solving Equations with Rational Numbers Check It Out: Example 1C Solve. y = 90 C. 4.5 y = 4.5 • 90 4.5 • 4.5 y = 405 Use the Multiplication Property of Equality. Multiply both sides by 4.5 2-7 Solving Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions Solve. 3 2 n+ =– 7 7 2 2 3 2 n– + =– – 7 7 7 7 n=– 5 7 2 Subtract from both sides. 7 2-7 Solving Equations with Rational Numbers Additional Example 2B: Solving Equations with Fractions Solve. 1 2 y– = 6 3 1 y 1 2 1 + – = + 6 6 3 6 4 1 y= + 6 6 5 y= 6 1 Add to both sides. 6 Find a common denominator; 6. Simplify. 2-7 Solving Equations with Rational Numbers Additional Example 2C: Solving Equations with Fractions Solve. 5 5x = 8 6 5 Divide both sides by . 6 Simplify. 2-7 Solving Equations with Rational Numbers Check It Out: Example 2A Solve. 5 1 =– 9 9 1 1 5 1 n– + =– – 9 9 9 9 2 n=– 3 n+ 1 Subtract 9 from both sides. 6 Simplify – . 9 2-7 Solving Equations with Rational Numbers Check It Out: Example 2B Solve. 1 3 y– 2 = 4 1 y 1 3 1 + – = + 2 2 4 2 3 2 + 4 4 1 y=1 4 y= 1 Add to both sides. 2 Find a common denominator; 4. Simplify. 2-7 Solving Equations with Rational Numbers Check It Out: Example 2C Solve. 6 3x = 19 8 Divide both sides by x = 16 19 Simplify. 3 . 8 2-7 Solving Equations with Rational Numbers Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 2-7 Solving Equations with Rational Numbers Lesson Quiz: Part I Solve. 1. x – 23.3 = 17.8 x = 41.1 3 2 2. j + = –14 4 3 5 j = –15 12 3. 9y = 3 5 y= 1 15 d = 23 4. 4 8 1 d=9 2 2-7 Solving Equations with Rational Numbers Lesson Quiz: Part II 2 5. Tamara can mow 5 acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5 hours 2-7 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 1. Solve. a – 36 = 44.9 A. a = 36.7 B. a = 49.2 C. a = 59.9 D. a = 80.9 2-7 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 2. Solve. c + 3 = –11 4 4 5 A. c = 12 11 20 C. c = 11 4 5 B. c = –12 11 20 D. c = 113 4 2-7 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 3. Solve. 8e = 2 3 A. e = 8 2 3 C. e = 1 12 B. e = 5 1 3 D. e = 3 20 2-7 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 4. Solve. h = 35 3 6 A. h = 9 1 2 C. h = 11 1 2 B. h = 10 1 2 D. h = 12 1 2