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Warm Up Solve. 1. x + 12 = 35 2. 8 x = 120 3. = 7 4. –34 = y + 56

y 9. Warm Up Solve. 1. x + 12 = 35 2. 8 x = 120 3. = 7 4. –34 = y + 56. x = 23. x = 15. y = 63. y = –90.

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Warm Up Solve. 1. x + 12 = 35 2. 8 x = 120 3. = 7 4. –34 = y + 56

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  1. y9 Warm Up Solve. 1.x + 12 = 35 2. 8x = 120 3.= 7 4. –34 = y + 56 x = 23 x = 15 y = 63 y = –90

  2. Recall that two-step equations contain two operations, and therefore, require two inverse operations to solve. Before solving, ask yourself, “What is being done to the variable, and in what order?” One method to solve the equation is to work backward to undo the operations.

  3. n3 n3 n3 n3 n3 n3 + 7 = 22 = 15 Since 7 is added to , subtract 7 from both sides to undo the addition. + 7 – 7= 22 – 7 3 = 3  15 Additional Example 2A: Solving Two-Step Equations Solve + 7 = 22. Use fraction operations. Since n is divided by 3, multiply both sides by 3. n = 45

  4. y – 4 y – 4 y – 4 3 3 3 = 9 = 9 (3) (3) Additional Example 2B: Solving Two-Step Equations Solve = 9. Multiply both sides of the equation by the denominator. Multiply both sides by the denominator. y – 4 = 27 + 4+ 4Since 4 is subtracted from y, add 4 to both sides to undo the subtraction. y = 31

  5. n4 n4 n4 n4 n4 n4 + 8 = 18 = 10 Since 8 is added to , subtract 8 from both sides to undo the addition. + 8 – 8= 18 – 8 4 = 4  10 Partner Share! Example 2A Solve + 8 = 18. Use fraction operations. Since n is divided by 4, multiply both sides by 4. n = 40

  6. y – 7 y – 7 y – 7 2 2 2 = 7 = 7 (2) (2) Partner Share! Example 2B Solve = 7. Multiply both sides of the equation by the denominator. Multiply both sides by the denominator. y – 7 = 14 + 7+ 7Since 7 is subtracted from y, add 7 to both sides to undo the subtraction. y = 21

  7. Additional Example 1: Problem Solving Application The mechanic’s bill to repair Mr. Wong’s car was $653.05. The mechanic charges $45.50 an hour for labor, and the parts that were used cost $443.75. How many hours did the mechanic work on the car?

  8. 1 Understand the Problem Additional Example 1 Continued List the important information: The answer is the number of hours the mechanic worked on the car. • The parts cost $443.75. • The labor cost $45.50 per hour. • The total bill was $653.05. Let h represent the hours the mechanic worked. Total bill = Parts + Labor 653.05 = 443.75 + 45.50h

  9. Make a Plan 2 Additional Example 1 Continued Think: First the variable is multiplied by 45.50, and then 443.75 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443.75 from both sides of the equation, and then divide both sides of the new equation by 45.50.

  10. 3 Solve 209.30 45.50h = 45.5045.50 Additional Example 1 Continued Since 443.75 is added to both sides, subtract 443.75 from both sides. 653.05 = 443.75 + 45.50h –443.75–443.75 209.30 = 45.50h Since h is multiplied by 45.50, divide both sides by 45.50. 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong’s car.

  11. 4 Look Back Additional Example 1 Continued You can use a table to decide whether your answer is reasonable. 4.6 hours is a reasonable answer.

  12. Partner Share! Example 1 The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?

  13. 1 Understand the Problem Partner Share! Example 1 Continued List the important information: The answer is the number of hours the mechanic worked on your car. • The parts cost $275. • The labor cost $35 per hour. • The total bill was $850. Let h represent the hours the mechanic worked. Total bill = Parts + Labor 850 = 275 + 35h

  14. 3 Solve 575 35h = 3535 Partner Share! Example 1 Continued Since 275 is added to both sides, subtract 275 from both sides. 850 = 275 + 35h –275–275 575 = 35h Since h is multiplied by 35, divide both sides by 35. 16.4 h The mechanic worked for about 16.4 hours on your car.

  15. 4 Look Back Partner Share! Example 1 Continued You can use a table to decide whether your answer is reasonable. 16.4 hours is a reasonable answer.

  16. 1 9 y + 5 11 Lesson Review! Solve. 1. – x – 3 = 10 2. 7y + 25.68 = –26.12 3. –8.3 = –3.5x + 13.4 4. = 3.1 5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1032.96, how many months will the contract last? x = –117 y = –7.4 x = 6.2 y = 29.1 24 months

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