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Solving Two-Step Equations. 10-1. Homework & Learning Goal. Lesson Presentation. AIMS Prep. Pre-Algebra. Pre-Algebra HOMEWORK. Page 500 #8-30 EVENS. Our Learning Goal.

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10-1

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  1. Solving Two-Step Equations 10-1 Homework & Learning Goal Lesson Presentation AIMS Prep Pre-Algebra

  2. Pre-Algebra HOMEWORK Page 500 #8-30 EVENS

  3. Our Learning Goal Students will be able to solve multi-step equations with multiple variables, solve inequalities and graph the solutions on a number line.

  4. Our Learning Goal Assignments • Learn to solve two-step equations. • Learn to solve multistep equations. • Learn to solve equations with variables on both sides of the equal sign. • Learn to solve two-step inequalities and graph the solutions of an inequality on a number line. • Learn to solve an equation for a variable. • Learn to solve systems of equations.

  5. Today’s Learning Goal Assignment Learn to solve 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 & in what order?” Then work backward to undo the operations.

  7. 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?

  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. • 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

  9. 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.

  10. 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.

  11. 4 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.

  12. 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?

  13. 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

  14. Make a Plan 2 Try This: 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.

  15. 3 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.

  16. 4 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.

  17. n3 n3 n3 n3 + 7 = 22 = 15 Multiply to undo division. 3 = 3  15 Additional 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

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

  19. 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

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

  21. –3.9 = –1.3m –1.3 –1.3 Additional 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

  22. 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

  23. C. = 9 y – 4 y – 4 y – 4 3 3 3 = 9 = 9 3 ·3 ·Multiply to undo division. Additional 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

  24. 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

  25. x –9 y + 5 11 Don’t forget your proper heading! Trade & Grade! 10-1 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

  26. 6th Grade AIMS Prep When you play a game with a friend, there are lots of tricks, or strategies, that you use to win the game. Just like the game tricks, there are lots of test-taking tricks to help you “win” when taking the AIMS Math Test. What are some test-taking tricks that you use?

  27. AIMS Example 1What is the problem asking us to solve?

  28. Test-Taking Strategy #1Understand the problem!! Read It Thoroughly!

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