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# Chapter2.7

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### Chapter2.7

1. 1. Warm Up California Standards Lesson Presentation Preview
2. 2. Warm Up Add or subtract. + 1. 5 10 2. 5 16 2 – 1 3. 4.8 + 3.6 4. 2.4 – 0.05 8.4 2.35 7 10 3 8 1 5 1 1 16 1
3. 3. AF4.0 Students solve simple linear equations and inequalities over the rational numbers. California Standards
4. 4. m + 4.6 = 9 m + 4.6 = 9 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition. Additional Examples 1A: Solving Equations with Decimals Solve. 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! 4.4 m = – 4.6 – 4.6
5. 5. 8.2 p = –32.8 Since p is multiplied by 8.2, divide both sides by 8.2. Additional Examples 1B: Solving Equations with Decimals Solve. – 4 p = – 32.8 8.2 8.2 p 8.2 =
6. 6. Additional Examples 1C: Solving Equations with Decimals x = 18 Since x is divided by 1.2, multiply both sides by 1.2. Solve. = 15 x 1.2 x 1.2 = 1.2 • 15 1.2 •
7. 7. m + 9.1 = 3 m + 9.1 = 3 Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition. Check It Out! Example 1 Solve. A. B. 5.5 b = 75.9 Since b is multiplied by 5.5, divide both sides by 5.5. – 6.1 m = – 9.1 = – 9.1 75.9 5.5 5.5 5.5 = b 13.8 b =
8. 8. = 90 Check It Out! Example 1C y = 405 Since y is divided by 4.5, multiply both sides by 4.5. y 4.5 Solve. C. y 4.5 = 4.5 • 90 4.5 •
9. 9. Additional Example 2A: Solving Equations with Fractions Solve. = – 3 7 n + 2 7 n + – = – – 3 7 2 7 27 27 n = – 5 7 2 7 Since is added to n, subtract from both sides. 2 7
10. 10. 1 6 = 2 3 y – Additional Example 2B: Solving Equations with Fractions Find a common denominator, 6. Solve. = y 4 6 1 6 + = y – 2 3 1 6 Since is subtracted from y, add to both sides. 1 6 1 6 + 1 6 + 1 6 = y 5 6
11. 11. 5 6 = 5 8 x Multiply by the reciprocal. Simplify. Additional Example 2C: Solving Equations with Fractions 3 4 Solve. 1 1 1 1 1 1 5 6 = 5 8 x 6 5 • • 6 5 x = 3 4 Since x is multiplied by , divide both sides by . 5 6 5 6 5 6 ÷ = ÷ 5 8 x 5 6 5 6
12. 12. 1 9 = – 5 9 n + Check It Out! Example 2A Simplify. Solve. n = – 2 3 n + – = – – 5 9 1 9 19 19 n = – 6 9 1 9 Since is added to n, subtract from both sides. 1 9
13. 13. Check It Out! Example 2B Solve. Simplify. Find a common denominator, 4. y = 1 1 4 = y – 1 2 3 4 = y 3 4 2 4 + = y – 3 4 1 2 Since is subtracted from y, add to both sides. 1 2 1 2 + 1 2 + 1 2 = y 5 4
14. 14. Check It Out! Example 2C Solve. 3 8 = 3 4 x Multiply by the reciprocal. Simplify. x = 2 2 1 1 1 1 1 1 1 3 8 = 3 4 x 8 3 • • 8 3 Since x is multiplied by , divide both sides by . 3 8 3 8 3 8 ÷ = ÷ 3 4 x 3 8 3 8
15. 15. Write an equation: Amount Needed 1/3 Amount Saved Additional Example 3: Solving Word Problems Using Equations  = Janice has saved \$21.40. This is of what she needs to save to buy a new piece of software. What is the total amount that Janice needs to save? a  = \$21.40 1 3 1 3
16. 16. Additional Example 3 Continued Janice needs to save \$64.20. Multiply by the reciprocal. Simplify. 1 3 = 21.40  a   3 1 3 1 a = 64.20 Since a is multiplied by , divide both sides by . 1 3 1 3 = 21.40 ÷ a x ÷ 1 3 1 3 1 3
17. 17. Write an equation: Capacity of minivan’s tank 2/3 Capacity of car’s tank • = Check It Out! Example 3 g • = 24 2 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 24 gallons of gasoline, how much gasoline can the tank in the minivan hold? 2 3
18. 18. Check It Out! Example 3 Continued The minivan can hold 36 gallons of gas. Multiply by the reciprocal. Simplify. 2 3 = 24  g   3 2 3 2 g = 36 Since g is multiplied by , divide both sides by . 2 3 2 3 = 24 ÷ g  ÷ 2 3 2 3 2 3 g = 722
19. 19. Lesson Quiz Solve. 1. x – 23.3 = 17.8 2. j + = –14 3. 9 y = 4. x = 41.1 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? 5. 5 hours 1 15 y = j = – 15 5 12 3 4 3 5 d 4 = 2 3 8 2 3 1 2 d = 9 2 5