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

2. Pre-Algebra 10-1 Solving Two-Step Equations Pre-Algebra HOMEWORK Page 500 #8-30 EVENS

3. Pre-Algebra 10-1 Solving Two-Step Equations 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. Pre-Algebra 10-1 Solving Two-Step Equations 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. Pre-Algebra 10-1 Solving Two-Step Equations Today’s Learning Goal Assignment Learn to solve two-step equations.

6. Pre-Algebra 10-1 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 Pre-Algebra 10-1 Solving Two-Step Equations y = –90 y9y9

7. Pre-Algebra 10-1 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 x? (Hint: Think about what the prime number must be in order for x to be an odd.) x = 3

8. Pre-Algebra 10-1 Solving Two-Step Equations Today’s Learning Goal Assignment Learn to solve two-step equations.

9. Pre-Algebra 10-1 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 & in what order?” Then work backward to undo the operations.

10. Pre-Algebra 10-1 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

11. Pre-Algebra 10-1 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

12. Pre-Algebra 10-1 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

13. Pre-Algebra 10-1 Solving Two-Step Equations 650 = 443 + 45h Solve 3 –443 –443Subtract 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 Divide to undo multiplication. 207 45h 45 =

14. Pre-Algebra 10-1 Solving Two-Step Equations 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. Look Back4 Additional Example 1 Continued

15. Pre-Algebra 10-1 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? Try This: Example 1

16. Pre-Algebra 10-1 Solving Two-Step Equations Try This: 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

17. Pre-Algebra 10-1 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 Try This: Example 1 Continued

18. Pre-Algebra 10-1 Solving Two-Step Equations 850 = 275 + 35h Solve 3 –275 –275Subtract to undo the addition. 575= 35h 16.4  h The mechanic worked for about 16.4 hours on your car. Try This: Example 1 Continued Divide to undo multiplication. 575 35h 35 =

19. Pre-Algebra 10-1 Solving Two-Step Equations 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. Look Back4 Try This: Example 1 Continued

20. Pre-Algebra 10-1 Solving Two-Step Equations Additional Example 2A: Solving Two-Step Equations A. + 7 = 22 Solve. 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 – 7 Subtract to undo addition. n3n3 + 7 = 22 n3n3 Multiply to undo division. 3  = 3  15 n3n3 n = 45 n3n3 = 15

21. Pre-Algebra 10-1 Solving Two-Step Equations Additional Example 2A Continued Substitute 45 into the original equation. Check + 7 = 22 n3n3 ? 45 3 15 + 7 = 22 ?

22. Pre-Algebra 10-1 Solving Two-Step Equations Try This: Example 2A A. + 5 = 29 Solve. 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 – 5 Subtract to undo addition. n4n4 + 5 = 29 n4n4 Multiply to undo division. 4  = 4  24 n4n4 n = 96

23. Pre-Algebra 10-1 Solving Two-Step Equations Substitute 96 into the original equation. Check + 5 = 29 n4n4 ? 96 4 24 + 5 = 29 ? Try This: Example 2A Continued

24. Pre-Algebra 10-1 Solving Two-Step Equations 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 Subtract to undo addition. –3.9 = –1.3m Divide to undo multiplication. 3 = m –1.3 –3.9 = –1.3m

25. Pre-Algebra 10-1 Solving Two-Step Equations 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 Subtract to undo addition. 4.6 = –2.3m Divide to undo multiplication. –2 = m –2.3 4.6 = –2.3m

26. Pre-Algebra 10-1 Solving Two-Step Equations Additional Example 2C: Solving Two-Step Equations C. = 9 y – 4 3 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. = 9 y – 4 3 y – 4 = 27 + 4 + 4Add to undo subtraction. y = 31 3 · 3 · Multiply to undo division.= 9 y – 4 3

27. Pre-Algebra 10-1 Solving Two-Step Equations Try This: Example 2C C. = 8 y – 2 4 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. = 8 y – 2 4 y – 2 = 32 + 2 + 2Add to undo subtraction. y = 34 4 · 4 · Multiply to undo division.= 8 y – 2 4

28. Pre-Algebra 10-1 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? Don’t forget your proper heading! Trade & Grade! 10-1 Lesson Quiz y = –7 x = –117 x = 6.2 y = 28 24 months x –9 y + 5 11

29. Pre-Algebra 10-1 Solving Two-Step Equations 6 th 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?

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

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