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2-8 Solving Two-Step Equations Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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2-8 Solving Two-Step Equations Warm Up Solve. 1. x + 12 = 35 2. 8x = 120 3. = 7 4. –34 = y + 56 x = 23 x = 15 y = 63 y = –90 y9y9

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2-8 Solving Two-Step Equations 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

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2-8 Solving Two-Step Equations Learn to solve two-step equations.

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2-8 Solving Two-Step Equations 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.

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2-8 Solving Two-Step Equations 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? Additional Example 1: Problem Solving Application

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2-8 Solving Two-Step Equations Additional Example 1 Continued 1 Understand the Problem The answer is the number of hours the mechanic worked on the car. List the important information: Let h represent the hours the mechanic worked. The parts cost $443. The labor cost $45 per hour. The total bill was $650. Total bill=Parts+Labor 650 = 443 + 45h

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2-8 Solving Two-Step Equations 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. 2 Make a Plan Additional Example 1 Continued

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2-8 Solving Two-Step Equations 650 = 443 + 45h Solve 3 –443 –443 Step 1: Subtract to undo the addition. 207= 45h 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong’s car. Additional Example 1 Continued Step 2: Divide to undo multiplication. 207 45h 45 =

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2-8 Solving Two-Step Equations You can use a table to decide whether your answer is reasonable. Look Back4 Additional Example 1 Continued $668$4432255 $623$4431804 $578$4431353 $533$443902 $488$443451 Total CostPartsLaborHours 4.6 hours is a reasonable answer.

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2-8 Solving Two-Step Equations 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? Check It Out: Example 1

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2-8 Solving Two-Step Equations Check It Out: Example 1 Continued 1 Understand the Problem The answer is the number of hours the mechanic worked on your car. List the important information: Let h represent the hours the mechanic worked. The parts cost $275. The labor cost $35 per hour. The total bill was $850. Total bill=Parts+Labor 850=275+35h

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2-8 Solving Two-Step Equations 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. 2 Make a Plan Check It Out: Example 1 Continued

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2-8 Solving Two-Step Equations 850 = 275 + 35h Solve 3 –275 –275 Step 1: Subtract to undo the addition. 575= 35h 16.4 h The mechanic worked for about 16.4 hours on your car. Check It Out: Example 1 Continued Step 2: Divide to undo multiplication. 575 35h 35 =

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2-8 Solving Two-Step Equations Look Back4 Check It Out: Example 1 Continued You can use a table to decide whether your answer is reasonable. $870$27559517 $835$27556016 $800$27552515 $765$27549014 $730$27545513 Total CostPartsLaborHours 16.4 hours is a reasonable answer.

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2-8 Solving Two-Step Equations Additional Example 2A: Solving Two-Step Equations Solve + 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. Subtract 7 from both sides. n3n3 + 7 – 7 = 22 – 7 n3n3 Multiply both sides by 3. 3 = 3 15 n3n3 n = 45 Method 1: Work backward to isolate the variable.

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2-8 Solving Two-Step Equations Additional Example 2A Continued Multiply both sides by the denominator. + 7 = 22(3) n3n3 Subtract to undo addition. n + 21 = 66 n = 45 Method 2: Multiply both sides of the equation by the denominator. Solve + 7 = 22. n3n3 (3) –21 –21

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2-8 Solving Two-Step Equations Additional Example 2B: Solving Two-Step Equations Solve = 9. y – 4 3 Method 1: Work backward to isolate the variable. – = 9 y3y3 4343 Rewrite the expression as the sum of two fractions. Think: First the variable is divided by 3, and then is subtracted. To isolate the variable, add and then multiply by 3. 4343 4343 4343 – + = 9 + y3y3 4343 4343 (3) = (3) y3y3 31 t3 Add to both sides. 4343 Multiply both sides by 3. y = 31

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2-8 Solving Two-Step Equations Additional Example 2B Continued Solve = 9. y – 4 3 = 9 y – 4 3 y – 4 = 27 + 4 + 4Add to undo subtraction. y = 31 Multiply both sides by the denominator. Method 2: Multiply both sides of the equation by the denominator. = 9 y – 4 3 (3)

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2-8 Solving Two-Step Equations Check It Out: Example 2A Solve + 8 = 18. Think: First the variable is divided by 4, and then 8 is added. To isolate the variable, subtract 8, and then multiply by 4. Subtract 8 from both sides. n4n4 + 8 – 8 = 18 – 8 n4n4 Multiply both sides by 4. 4 = 4 10 n4n4 n = 40 Method 1: Work backward to isolate the variable.

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2-8 Solving Two-Step Equations Check It Out: Example 2A Continued Multiply both sides by the denominator. + 8 = 18(4) n4n4 Subtract to undo addition. n + 32 = 72 n = 40 Method 2: Multiply both sides of the equation by the denominator. Solve + 8 = 18. n4n4 (4) –32 –32

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2-8 Solving Two-Step Equations Check It Out: Example 2B Solve = 7. y – 7 2 Method 1: Work backward to isolate the variable. – = 7 y2y2 7272 Rewrite the expression as the sum of two fractions. Think: First the variable is divided by 2, and then is subtracted. To isolate the variable, add and then multiply by 2. 7272 7272 7272 – + = 7 + y2y2 7272 7272 (2) = (2) y2y2 21 t2 Add to both sides. 7272 Multiply both sides by 2. y = 21

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2-8 Solving Two-Step Equations Check It Out: Example 2B Continued Solve = 7. y – 7 2 = 7 y – 7 2 y – 7 = 14 + 7 + 7Add to undo subtraction. y = 21 Multiply both sides by the denominator. Method 2: Multiply both sides of the equation by the denominator. = 7 y – 7 2 (2)

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2-8 Solving Two-Step Equations Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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2-8 Solving Two-Step Equations 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? Lesson Quiz y = –7 x = –117 x = 6.2 y = 28 24 x –9 y + 5 11

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2-8 Solving Two-Step Equations 1. Solve – 9 = 3. A. p = –84 B. p = –42 C. p = 42 D. p = 84 Lesson Quiz for Student Response Systems p -7

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2-8 Solving Two-Step Equations 2. Solve 3r + 46 = –29. A. r = –20 B. r = –25 C. r = –30 D. r = –35 Lesson Quiz for Student Response Systems

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2-8 Solving Two-Step Equations 3. Solve –3.3 = –1.2t + 15.3. A. t = 15.5 B. t = 14 C. t = 12.5 D. t = 10 Lesson Quiz for Student Response Systems

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2-8 Solving Two-Step Equations 4. Solve = 5. A. v = 31 B. v = 32 C. v = 33 D. v = 34 Lesson Quiz for Student Response Systems v + 7 8

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2-8 Solving Two-Step Equations 5. The membership fee of a DVD rental store is $15. The cost of renting a DVD is $2. If John pays $27, how many DVDs did he rent? A. 6 DVDs B. 8 DVDs C. 12 DVDs D. 24 DVDs Lesson Quiz for Student Response Systems

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