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2-8

Solving Two-Step Equations. 2-8. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 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. Problem of the Day

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2-8

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  1. Solving Two-Step Equations 2-8 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 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

  3. Problem of the Day x is an odd integer. If you triple x and then subtract 7, you get a prime number. What is the smallest possible x? (Hint: What is the smallest prime number?) x = 3

  4. Learn to solve two-step equations.

  5. 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.

  6. Additional 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?

  7. 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

  8. Make a Plan 2 Additional Example 1 Continued Think: First the variable is multiplied by 45, and then 443 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443 from both sides of the equation, and then divide both sides of the new equation by 45.

  9. 3 Solve 207 45h = 4545 Additional 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.

  10. 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.

  11. Check It Out: 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?

  12. 1 Understand the Problem Check It Out: 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

  13. Make a Plan 2 Check It Out: Example 1 Continued Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35.

  14. 3 Solve 575 35h = 3535 Check It Out: 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.

  15. 4 Look Back Check It Out: Example 1 Continued You can use a table to decide whether your answer is reasonable. 16.4 hours is a reasonable answer.

  16. n3 n3 n3 + 7 – 7= 22 – 7 3 = 3  15 Additional Example 2A: Solving Two-Step Equations Solve + 7 = 22 Method 1: Work backward to isolate the variable. Think: First the variable is divided by 3, and then 7is added. To isolate the variable, subtract 7, and then multiply by 3. Subtract 7 from both sides. Multiply both sides by 3. n = 45

  17. n3 n3 + 7 = 22(3) Additional Example 2A Continued Solve + 7 = 22 Method 2: Multiply both sides of the equation by the denominator. (3) Multiply both sides by the denominator. n + 21 = 66 Subtract to undo addition. –21–21 n = 45

  18. 43 43 y3 43 y3 43 43 31 t3 y3 43 43 y – 4 3 Think: First the variable is divided by 3, and thenis subtracted. To isolate the variable, add and then multiply by 3. – = 9 Add to both sides. – + = 9 + (3) = (3) Additional Example 2B: Solving Two-Step Equations Solve = 9 Method 1: Work backward to isolate the variable. Rewrite the expression as the sum of two fractions. Multiply both sides by 3. y = 31

  19. y – 4 y – 4 y – 4 3 3 3 = 9 = 9 (3) (3) Additional Example 2B: Solving Two-Step Equations Solve = 9 Method 2: Multiply both sides of the equation by the denominator. Multiply both sides by the denominator. y – 4 = 27 + 4+ 4Add to undo subtraction. y = 31

  20. n4 n4 n4 + 8 – 8= 18 – 8 4 = 4  10 Check It Out: Example 2A Solve + 8 = 18 Method 1: Work backward to isolate the variable. Think: First the variable is divided by 4, and then 8is added. To isolate the variable, subtract 8, and then multiply by 4. Subtract 8 from both sides. Multiply both sides by 4. n = 40

  21. n4 n4 + 8 = 18(4) Check It Out: Example 2A Solve + 8 = 18 Method 2: Multiply both sides of the equation by the denominator. (4) Multiply both sides by the denominator. n + 32 = 72 Subtract to undo addition. –32–32 n = 40

  22. 72 72 y2 72 y2 72 72 21 t2 y2 72 72 y – 7 2 Think: First the variable is divided by 2, and thenis subtracted. To isolate the variable, add and then multiply by 2. – = 7 Add to both sides. – + = 7 + (2) = (2) Check It Out: Example 2B Solve = 7 Method 1: Work backward to isolate the variable. Rewrite the expression as the sum of two fractions. Multiply both sides by 2. y = 21

  23. y – 7 y – 7 y – 7 2 2 2 = 7 = 7 (2) (2) Check It Out: Example 2B Solve = 7 Method 2: Multiply both sides of the equation by the denominator. Multiply both sides by the denominator. y – 7 = 14 + 7+ 7Add to undo subtraction. y = 21

  24. 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

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