1. 2-7 Solving Equations with Rational Numbers Learn to solve equations with rational numbers.

2. 2-7 Solving Equations with Rational Numbers m + 4.6 = 9 Use the Subtraction Property of Equality. Subtract 4.6 from both sides. 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. Remember! Additional Examples 1A: Solving Equations with Decimals Solve. 4.4 m = – 4.6 =

3. 2-7 Solving Equations with Rational Numbers 8.2p = –32.8 –4 p = Use the Division Property of Equality. Divide both sides by 8.2 –32.8 8.2 8.2p 8.2 = Additional Examples 1B: Solving Equations with Decimals Solve.

4. 2-7 Solving Equations with Rational Numbers Additional Examples 1C: Solving Equations with Decimals x = 18 Use the Multiplication Property of Equality. Multiply both sides by 1.2 = 15 x 1.2 = 1.2 15 1.2 Solve.

5. 2-7 Solving Equations with Rational Numbers m + 9.1 = 3 Use the Subtraction Property of Equality. Subtract 9.1 from both sides. Check It Out: Example 1A & 1B –6.1 m = –9.1 = Solve. A. B. 5.5b = 75.9 75.9 5.55.5 = b 13.8 b = Use the Division Property of Equality. Divide both sides by 5.5

6. 2-7 Solving Equations with Rational Numbers = 90 Check It Out: Example 1C y = 405 Use the Multiplication Property of Equality. Multiply both sides by 4.5 y 4.5 = 4.5 90 4.5 Solve. C.

7. 2-7 Solving Equations with Rational Numbers 2727 = – 3737 n + Additional Example 2A: Solving Equations with Fractions n – + = – – 2727 3737 2727 2727 n = – 5757 Subtract from both sides. 2727 Solve.

8. 2-7 Solving Equations with Rational Numbers 1616 = 2323 y – Additional Example 2B: Solving Equations with Fractions Find a common denominator; 6. y = 5656 =y 4646 1616 + 1616 = 2323 – 1616 + 1616 + y Add to both sides. 1616 Solve. Simplify.

9. 2-7 Solving Equations with Rational Numbers 5656 = 5858 x Simplify. Additional Example 2C: Solving Equations with Fractions Divide both sides by. 5656 Solve.

10. 2-7 Solving Equations with Rational Numbers 1919 = – 5959 n + Check It Out: Example 2A n – + = – – 1919 5959 1919 1919 n = – 2323 Subtract from both sides. 1919 Simplify –. 6969 Solve.

11. 2-7 Solving Equations with Rational Numbers 1212 = 3434 y – Check It Out: Example 2B Find a common denominator; 4. y = 1 1414 =y 3434 2424 + 1212 = 3434 – 1212 + 1212 + y Add to both sides. 1212 Solve. Simplify.

12. 2-7 Solving Equations with Rational Numbers Simplify. Check It Out: Example 2C Divide both sides by. 3838 x = 16 19 3838 = 6 19 x Solve.

13. 2-7 Solving Equations with Rational Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

14. 2-7 Solving Equations with Rational Numbers Lesson Quiz: Part I Solve. 1. x – 23.3 = 17.8 2. j + = –14 3. 9y = 4. 1 15 y = x = 41.1 3535 2323 3434 j = – 15 5 12 d 4 =2 3838 1 2 d = 9

15. 2-7 Solving Equations with Rational Numbers Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? Lesson Quiz: Part II 5. 5 hours 2525

16. 2-7 Solving Equations with Rational Numbers 1. Solve. a – 36 = 44.9 A. a = 36.7 B. a = 49.2 C. a = 59.9 D. a = 80.9 Lesson Quiz for Student Response Systems

17. 2-7 Solving Equations with Rational Numbers 2. Solve. c + = –11 A. c = 12C. c = 11 B. c = –12D. c = 11 Lesson Quiz for Student Response Systems 11 20 4545 3434 3434 4545

18. 2-7 Solving Equations with Rational Numbers 3. Solve. 8e = A. e = 8C. e = B. e = 5D. e = Lesson Quiz for Student Response Systems 2323 1313 1 12 3 20 2323

19. 2-7 Solving Equations with Rational Numbers 4. Solve. = 3 A. h = 9C. h = 11 B. h = 10D. h = 12 Lesson Quiz for Student Response Systems 1212 1212 1212 1212 h3h3 5656