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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. Two-Step Equations #6. Learn to solve two-step equations. Two-Step Equations #6.

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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. Two-Step Equations #6 Learn to solve two-step equations.

  3. Two-Step Equations #6 Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “What is being done to the variable, and in what order?” Then work backward to undo the operations. *Start with the operation further away from the variable- like untying a knot.

  4. n3 n3 n3 n3 + 7 = 22 = 15 Multiply to undo division. 3 = 3  15 Example 2A: Solving Two-Step Equations Solve. A. + 7 = 22 Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3. – 7– 7Subtract to undo addition. n = 45

  5. n3 + 7 = 22 453 ? + 7 = 22 ? 15 + 7 = 22 Additional Example 2A Continued Check Substitute 45 into the original equation. 

  6. –3.9 = –1.3m –1.3 –1.3 Example 2B: Solving Two-Step Equations B. 2.7 = –1.3m + 6.6 Think: First the variable is multiplied by –1.3, and then 6.6 is added. To isolate the variable, subtract 6.6, and then divide by –1.3. 2.7 = –1.3m + 6.6 –6.6–6.6 Subtract to undo addition. –3.9 = –1.3m Divide to undo multiplication. 3 = m

  7. C. = 9 y – 4 y – 4 y – 4 3 3 3 = 9 = 9 3 ·3 ·Multiply to undo division. Example 2C: Solving Two-Step Equations Think: First 4 is subtracted from the variable, and then the result is divided by 3. To isolate the variable, multiply by 3, and then add 4. y – 4 = 27 + 4+ 4Add to undo subtraction. y = 31

  8. n4 n4 n4 + 5 = 29 Multiply to undo division. 4  = 4  24 Try This: Example 2A Solve. A. + 5 = 29 Think: First the variable is divided by 4, and then 5 is added. To isolate the variable, subtract 5, and then multiply by 4. – 5– 5Subtract to undo addition. n = 96

  9. n4 + 5 = 29 964 ? + 5 = 29 ? 24 + 5 = 29 Try This: Example 2A Continued Check Substitute 96 into the original equation. 

  10. 4.6 = –2.3m –2.3 –2.3 Try This: Example 2B B. 4.8 = –2.3m + 0.2 Think: First the variable is multiplied by –2.3, and then 0.2 is added. To isolate the variable, subtract 0.2, and then divide by –2.3. 4.8 = –2.3m + 0.2 –0.2–0.2 Subtract to undo addition. 4.6 = –2.3m Divide to undo multiplication. –2 = m

  11. C. = 8 y – 2 y – 2 y – 2 4 4 4 = 8 = 8 4 ·4 ·Multiply to undo division. Try This: Example 2C Think: First 2 is subtracted from the variable, and then the result is divided by 4. To isolate the variable, multiply by 4, and then add 2. y – 2 = 32 + 2+ 2Add to undo subtraction. y = 34

  12. Example 1: Problem Solving Application The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 an hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?

  13. 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. • The labor cost $45 per hour. • The total bill was $650. Let h represent the hours the mechanic worked. Total bill = Parts + Labor 650 = 443 + 45h

  14. 2 Solve 207 45h = 4545 Example 1 Continued 650 = 443 + 45h –443–443Subtract to undo the addition. 207 = 45h Divide to undo multiplication. 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong’s car.

  15. 3 Look Back Additional Example 1 Continued If the mechanic worked 4.6 hours, the labor would be $45(4.6) = $207. The sum of the parts and the labor would be $443 + $207 = $650.

  16. Try This: 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?

  17. 1 Understand the Problem Try This: 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

  18. 2 Solve 575 35h = 3535 Try This: Example 1 Continued 850 = 275 + 35h –275–275Subtract to undo the addition. 575 = 35h Divide to undo multiplication. 16.4 h The mechanic worked for about 16.4 hours on your car.

  19. 3 Look Back Try This: Example 1 Continued If the mechanic worked 16.4 hours, the labor would be $35(16.4) = $574. The sum of the parts and the labor would be $275 + $574 = $849.

  20. x –9 y + 5 11 Lesson Quiz Solve. 1. – 3 = 10 2. 7y + 25 = –24 3. –8.3 = –3.5x + 13.4 4. = 3 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 $1014, how many months will the contract last? x = –117 y = –7 x = 6.2 y = 28 24 months

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