1. Solving Equations

2. Then/Now You translated sentences into equations. Solve equations by using addition and subtraction. Solve equations by using multiplication and division.

3. equivalent equations Vocabulary solve an equation

4. Example 1 Solve by Adding Solve h – 12 = –27. Then check your solution. h – 12 = –27Original equation h – 12 + 12 = –27 + 12Add 12 to each side. h = –15Simplify. Answer: h = –15

5. Concept 1

6. Example 1 Solve by Adding To check that –15 is the solution, substitute –15 for h in the original equation. h – 12 = –27Original equation –27 = –27Simplify. –15 – 12 = –27Replace h with –15. ?

7. Example 1 A.40 B.–8 C.8 D.–40 Solve a – 24 = 16. Then check your solution.

8. Example 2 Solve by Subtracting Solve c + 102 = 36. Then check your solution. c + 102 = 36Original equation c + 102 – 102 = 36 – 102Subtract 102 from each side. Answer: c = –66 To check that –66 is the solution, substitute –66 for c in the original equation. c + 102 = 36Original equation –66 + 102 = 36Replace c with –66. 36= 36Simplify.

9. Concept 2

10. Example 2 A.87 B.–171 C.171 D.–87 Solve 129 + k = –42. Then check your solution.

11. Example 3 Solve by Multiplying and Dividing A. 39 = -3r

12. Example 3 Solve by Multiplying and Dividing B.

13. Concept 3

14. Example 3 Solve by Multiplying and Dividing B. Solve –75 = –15b. –75 = –15bOriginal equation Answer: 5 = b 5 = bCheck the result. Divide each side by –15.

15. Example 3 Solve by Multiplying and Dividing A. Rewrite the mixed number as an improper fraction.

16. Example 3 Solve by Multiplying and Dividing

17. Example 3 A. B. C. D.5

18. Example 3 B. Solve 32 = –14c. A.–3 B.46 C.18 D.

19. Example 4 Solve by Multiplying TRAVEL Ricardo is driving 780 miles to Memphis. He drove about of the distance on the first day. About how many miles did Ricardo drive?

20. Example 4 Solve by Multiplying Answer: Ricardo drove about 468 miles on the first day. Multiply. Simplify. Original equation

21. Example 4 A.4 h B.6 h C.8 h D.16 h Water flows through a hose at a rate of 5 gallons per minute. How many hours will it take to fill a 2400-gallon swimming pool?

22. Summing UP: Solving an equation means finding the value of the variable in the equation that makes the equation true. To solve an equation, isolate the variable (with a coefficient of 1) on one side of the equation. (ISOLATE) Use the Properties of Equality to maintain equivalent equations in each step in this process. UNDO The Addition/Subtraction Property of Equality permits the same number to be added/subtracted to each side of an equation. The Multiplication/Division Property of Equality permits each side of an equation to be multiplied/divided by the same nonzero number.

23. Skills Practice – Grudge Match