2. Chapter 3 Review Day 2

3. Algebraic Equations Multiplication with Subtraction 2x – 4 = 8 +4 2x=12 22 x=6

4. Algebraic Equations Multiplication with Addition 5x + 10 = 80 -10 5x=70 55 x=14

5. Algebraic Equations Multiplication with Subtraction -3x – 4 = -82 +4 -3x=-78 -3 x=26

6. Algebraic Equations Multiplication with Addition 2/3x + 2 = 8 -2 x=6 x=18/2 = 9 2323 (HINT) Reciprocal 3232 3232

7. Algebraic Equations Division with Addition x/5 + 2 = 8 -2 =6 x=30 x5x5 (5)

8. Algebraic Equations C.L.T. -20 10x = 60 10 4x +6x + 20 = 80 ( ) 10x + 20 = 80 10 x = 6

9. Algebraic Equations C.L.T. -12 5x = 80 5 3x + 2x + 20 - 8 = 92 5x + 12 = 92 5 x = 16 ( ) ( )

10. Algebraic Equations C.L.T. -12 2x + 12 = 122 2 6x + 15 = 125 + 4x 6x – 4x + 12 = 122 + 4x – 4x 2 2x = 110 ( ) X = 55

11. ( ) 10x – 3x -12 = 4x – 9x + 48 Algebraic Equations Distributive Property 7x - 12 = -5x + 48 2(5x – 6) – 3x = 4(x + 12) – 9x 10x – 12 - 3x = 4x + 48 – 9x ( ) 7x + 5x - 12 = 48 12x - 12 = 48 ( )

12. 12 7x + 5x - 12 = 48 12x - 12 = 48 +12 12x = 60 X = 5 Algebraic Equations Distributive Property

13. Lesson 3.3, For use with pages 148-153 1.Simplify the expression 9x + 2(x – 1) + 7. ANSWER 11x + 5 2.5g – 7 = 58 ANSWER 13 Solve the equation.

14. Lesson 3.3, For use with pages 148-153 ANSWER 4 h Solve the equation. x 3. 2 3 = 18 27 4. A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225. Find the number of hours she spent surfing.

15. Daily Homework Quiz For use after Lesson 3.2 Solve the equation. 1. + 6 = –14 a 4 ANSWER80– 2. 6r – 12 = 6 ANSWER3 3. 36 = 7y 2y + – ANSWER 4–

16. Daily Homework Quiz For use after Lesson 3.2 The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is –6. 4. ANSWERy = 3x 9; 1 – A bank charges $5.00 per month plus $.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month. 5. ANSWER 11 checks

17. Solve an equation by combining like terms EXAMPLE 1 Solve 8x – 3x – 10 = 20. 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – 10 + 10 = 20 + 10 Add 10 to each side. 5x = 30 Simplify. Divide each side by 5. x = 6 Simplify. = 30 5 5x5x 5

18. EXAMPLE 2 Solve an equation using the distributive property Solve 7x + 2(x + 6) = 39. SOLUTION When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally.

19. EXAMPLE 2 METHOD 1 Show All Steps 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x + 12 – 12 = 39 – 12 9x = 27 x = 3 = 9x9x 9 27 9 METHOD 2 Do Some Steps Mentally 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x = 27 x = 3

20. Standardized Test Practice EXAMPLE 3 ANSWER The correct answer is D. A CD B SOLUTION In Step 2, the distributive property is used to simplify the left side of the equation. Because –4(x – 3) = –4x + 12, Step 2 should be 5x – 4x + 12 = 17.

21. GUIDED PRACTICE for Examples 1, 2, and 3 9d – 2d + 4 = 32 1. Solve the equation. Check your solution. 4ANSWER

22. EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 2w + 3(w + 4) = 27 2. 3ANSWER Solve the equation. Check your solution.

23. EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 6x – 2(x – 5) = 46 3. 9ANSWER Solve the equation. Check your solution.

24. Multiply by a reciprocal to solve an equation EXAMPLE 4 Write original equation. 3 2 (3x + 5) = –24 2 3 3 2 (3x + 5) = (–24) 2 3 Multiply each side by, the reciprocal of. 2 3 3 2 3x + 5 = –16 Simplify. 3x = –21 Subtract 5 from each side. x = –7 Divide each side by 3. 3 2 (3x + 5) = –24 Solve.

25. Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example 4 3 4 (z – 6) = 12 4. Solve the equation. Check your solution. 22ANSWER

26. Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example 4 2 5 (3r + 4) = 10 5. Solve the equation. Check your solution. 7ANSWER

27. Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example 4 6. 4 5 (4a – 1) = 28 – Solve the equation. Check your solution. –8.5ANSWER

28. There are actually three different possible outcomes when solving for a variable. 1. One solution 2. No Solutions 3. Infinitely Many Solutions

29. Let’s try some examples… Solve the following for the indicated variable: x = -8 No Solution Infinitely Many Solutions X =

30. Your Turn… Solve the following for the indicated variable: n = 20 Infinitely many Solutions x = -7 No Solutions

31. Warm up Solve the following for the indicated variable: 1. 2. 3. 4.

32. Warm up Answers 1. 2. 3. 4.

33. So, to change a percentage into a decimal, you always divide by 100 For example, 35% as a fraction is 35/100 so to change this into a decimal, you divide 35 by 100 35% 0.35 ÷ 100

34. To change decimal into a percentage DecimalPercentage To change a decimal into a percentage, you X by 100 0.23 23% X 100

35. Problem 1 Brittany Berrier became a famous skater. She won 85% of her meets. If she had 250 meets in 2000, how many did she win? 212.5 meets

36. Problem 2 Krystyl Ferguson worked at the zoo. If 3 of her 17 baboons were sick, What % were sick? About 18%

37. Problem 3 Matt Debord worked as a produce manager for Walmart. If 35 people bought green peppers and this was 28% of the total customers, how many customers did he have? 125

38. Problem 4 Emily Lower was a great WNBA ball player. They made $700,000 a year. If they owed 22% for taxes, how much did they pay in taxes? $154,000 in taxes

39. Problem 5 Tiffany Lowery got 65 referrals during the year. If 14% of these were for tardies, how many times did she get caught for being tardy? 9.1 tardies

40. Problem 6 Brett Mull became a famous D.J. He played a total of 185 C.D’s in January. If he played 35 classical C.D.’s, what is the percent of classical C.D.’s he played. About 19%

41. Problem 7 Brett Smith became a doctor. He fixed elephant trunks. He fixed 78.5% of all the elephants he treated. He fixed 45 elephant trunks. How many elephants did he treat in all. About 57.32 trunks

42. Problem 8 Ashley Scalf became a famous golfer. She did occasionally hit one into the pond. If she hit 7 out of 85 hits into the pond, what percentage did she hit into the pond. About 8.2%

43. Problem 9 Jeremy Devereaux got the nice guy award. If 42 people voted and Jeremy got 85% of the votes, how many people voted for Jeremy? About 35.7 people

44. Problem 10 Brad (the Bull) Denton and Daniel (Killer) McFalls joined the WWE. They won 16 of their 23 bouts. What percentage did they win. About 69.6%

45. Problem 11 Sarah Roderick and Erin Lanning became Las Vegas show girls. If they paid $45,000 in taxes and they made $3,000,000 per year, what percentage did they pay in taxes? 1.5%

48. EXAMPLE 5 Write and solve an equation GUIDED PRACTICE for Example 5 7. WHAT IF? Suppose the cranes take 12 days (288 hours) to travel the 2500 miles. How many hours of this migration are the cranes not flying? 188 hANSWER