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Course Solving Two-Step Equations A1.c How do I Solve Equations In One Variable, Including Equations Involving Absolute Values? Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

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Course 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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Course Solving Two-Step Equations Example 1: Solving Two-Step Equations Solve - 5n - 7 = 28 ***Work backwards to isolate the variable Think: First the variable is multiplied by -5, and then 7 is subtracted. To isolate the variable, add 7, and then divide by n – = Add 7 to both sides. -5n = 35Divide both sides by n = -7

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Course Solving Two-Step Equations Example 2 : 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 ***Work backwards to isolate the variable.

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Course Solving Two-Step Equations Check It Out: Example 2 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 ***Work backwards to isolate the variable.

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Course Solving Two-Step Equations Example 3: Solving Two-Step Equations Solve = 9 y – 4 3 = 9 y – 4 3 y – 4 = Add to undo subtraction. y = 31 Multiply both sides by the denominator. ***Multiply both sides of the equation by the denominator. = 9 y – 4 3 (3)

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Course Solving Two-Step Equations Check It Out: Example 3 Solve = 7 y – 7 2 = 7 y – 7 2 y – 7 = Add to undo subtraction. y = 21 Multiply both sides by the denominator. ***Multiply both sides of the equation by the denominator. = 7 y – 7 2 (2)

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Course Solving Two-Step Equations The mechanics bill to repair Mr. Wongs 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? Example 4: Problem Solving Application

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Course Solving Two-Step Equations Example 4 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 = h

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Course 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 Make a Plan Example 4 Continued

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Course Solving Two-Step Equations 650 = h Solve 3 –443 –443Subtract to undo the addition. 207= 45h 4.6 = h The mechanic worked for 4.6 hours on Mr. Wongs car. Example 4 Continued Divide to undo multiplication h 45 =

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Course Solving Two-Step Equations You can use a table to decide whether your answer is reasonable. Look Back4 Example 4 Continued HoursLaborPartsTotal Cost 145$443$ $443$ $443$ $443$ $443$ hours is a reasonable answer.

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Course Solving Two-Step Equations The mechanics 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 4

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Course Solving Two-Step Equations Check It Out: Example 4 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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Course 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 Make a Plan Check It Out: Example 4 Continued

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Course Solving Two-Step Equations 850 = h Solve 3 –275 –275Subtract to undo the addition. 575= 35h 16.4 h The mechanic worked for about 16.4 hours on your car. Check It Out: Example 4 Continued Divide to undo multiplication h 35 =

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Course Solving Two-Step Equations Look Back4 Check It Out: Example 4 Continued You can use a table to decide whether your answer is reasonable. HoursLaborPartsTotal Cost 13455$275$ $275$ $275$ $275$ $275$ hours is a reasonable answer.

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Course Solving Two-Step Equations Solve. 1. – 3 = y + 25 = –24 3. –8.3 = –3.5x = 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 = x –9 y

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