2. Student Learning Goal Chart Chapter 10

3. Pre-Algebra Learning Goal Students will understand solving linear equations and inequalities.

4. Students will understand solving linear equations and inequalities by being able to do the following: Learn to solve two-step equations (10.1)

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 Pre-Algebra HW Page 500 #15-32

7. Pre-Algebra 10-1 Solving Two-Step Equations 10-1 Solving Two-Step Equations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

8. 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

9. 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

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

11. 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, and in what order?” Then work backward to undo the operations.

12. 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

13. 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

14. 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

15. 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 =

16. 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

17. 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

18. 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

19. 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

20. 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 =

21. 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

22. 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

23. 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 ?

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 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

26. 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

27. 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

28. 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

29. 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

30. 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? Lesson Quiz y = –7 x = –117 x = 6.2 y = 28 24 months x –9 y + 5 11