Module 1 Topic C Solving Equations and Inequalities Lesson 10 - True and False Equations Example:

Transcription

1 Module 1 Topic C Solving Equations and Inequalities Lesson 10 - True and False Equations Example: 1

2 Example: 2

3 Example: Example: 3

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5 Module 1 Topic C Solving Equations and Inequalities Lesson 10 - True and False Equations Problem Set 1) 2) 3) 4) 5) 6) 7) 8) 9) Module 1 Topic C Solving Equations and Inequalities Lesson 11 - Solution Sets for Equations and Inequalities 5

6 Example: A preview of factoring a trinomial: Example: 6

7 Example: Words: Set Notation: Graphically: Example: 7

8 Words: Set Notation: Graphically: Example: 8

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10 Module 1 Topic C Solving Equations and Inequalities Lesson 11 - Solution Sets for Equations and Inequalities Problem Set 1) 2) 3) 4) 5) Review: Describe the following properties. 6) Associative: 7) Commutative: 8) Distributive: 10

11 Module 1 Topic C Solving Equations and Inequalities Lesson 12 - Solving Equations Answer the following questions: Example: 11

12 Module 1 Topic C Solving Equations and Inequalities Lesson 12 - Solving Equations Problem Set 1) 2) 3) 4) 5) 6) 12

13 Module 1 Topic C Solving Equations and Inequalities Lesson 13 - Some Potential Dangers When Solving Equations Example: Describe the property or method used to convert the equation from one line to the next. Why are we sure that the initial equation x(1 x) + 2x 4 = 8x 24 x 2 and the final equation 20 = 5x have the same solution? What is the common solution set to all these equations? Example: 13

14 Example: Example: Example: 14

15 Module 1 Topic C Solving Equations and Inequalities Lesson 13 - Some Potential Dangers When Solving Equations Problem Set 1) 2) 3) 15

16 Module 1 Topic C Solving Equations and Inequalities Lesson 14 - Solving Inequalities Example: 16

17 Example: Example: 17

18 Example: Example: 18

19 Example: 19

20 Module 1 Topic C Solving Equations and Inequalities Lesson 14 - Solving Inequalities Problem Set 1) 2) 3) 4) 5) 6) 20

21 Module 1 Topic C Solving Equations and Inequalities Lesson 15 - Solution Sets of Two or More Equations (or Inequalities) Joined by And or Or Example: 21

22 Example: 22

23 Example: Example: 23

24 Example: Example: a) b) Example: Example: 24

25 Module 1 Topic C Solving Equations and Inequalities Problem Set Lesson 15 - Solution Sets of Two or More Equations (or Inequalities) Joined by And or Or 1) 2) 3) 25

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27 Module 1 Topic C Solving Equations and Inequalities Lesson 16 Solving Equations and Inequalities with And or Or Let s watch this video (clip 4:07 through 6:36) Key Words: Union: Intersection: What is the main difference between an and inequality and an or inequality? 27

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30 Module 1 Topic C Solving Equations and Inequalities Lesson 16 Solving Equations and Inequalities with And or Or Problem Set

31 Module 1 Topic C Solving Equations and Inequalities Lesson 17 Equations Involving Factored Expressions Can we use the distributive property backwards (FACTOR USING GCF)? 1. 4x x What can we place in front of a set of parenthesis that when you distribute into the problem, the result would be 4x x? ( ) = 4x x x 2 16 x ( ) Now you try: Make up an expression that has already been distributed. Write the expression down. Can your neighbor figure out the backwards distribution? = ( ) 31

32 e. (HINT: use and or or ) f. (HINT: Un-distribute, factor by GCF) 32

33 g. (HINT: Re-write as a product of two binomials first) 2. Solve for x in each. a. b Solve for x: 5. 33

34 Module 1 Topic C Solving Equations and Inequalities Lesson 17 Equations Involving Factored Expressions Problem Set

35 3. b. Module 1 Topic C Solving Equations and Inequalities Lesson 18 Equations Involving a Variable Expression in the Denominator Find each solution: 16 = Show Work for this one: = Let s get NSPIRED! 0 = = UH OH! What happened? Undefined means that 35

36 For what value of x with the expression be undefined? 36

37 Module 1 Topic C Solving Equations and Inequalities Lesson 18 Equations Involving a Variable Expression in the Denominator Problem Set For what values of x with the expression be undefined?

38 5. Module 1 Topic C Solving Equations and Inequalities Lesson 19 Rearranging Formulas We can solve equations using the SEE-DO chart, even if there are no numbers: SEE DO Dist. Prop. CLT VBS

39 Example 2 39

40 Module 1 Topic C Solving Equations and Inequalities Lesson 19 Rearranging Formulas Problem Set 40

41 5. Module 1 Topic C Solving Equations and Inequalities Lesson 20 Solution Sets with Equations and Inequalities with Two Variables 41

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43 Module 1 Topic C Solving Equations and Inequalities Lesson 20 Solution Sets with Equations and Inequalities with Two Variables Problem Set 43

44 7x 3y = 21 Module 1 Topic C Solving Equations and Inequalities Lesson 21 Solution Sets with Equations and Inequalities with Two Variables 44

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47 Module 1 Topic C Solving Equations and Inequalities Lesson 21 Solution Sets with Equations and Inequalities with Two Variables Problem Set 2. 47

48 Module 1 Topic C Solving Equations and Inequalities Lesson 22 Systems of Equations (Graphing & Substitution) & Systems of Inequalities Work on a. through c. on your own. d. e. Describe the solution set to x + y > 10 and y = 2x

49 Example: Example: Solve by graphing and by using an algebraic method. 49

50 Solve by graphing. Solve by graphing. Were you able to find an exact solution from the graph? How can you tell when a system of equations will have no solution from the graph? What if a system of linear equations had the same slope and the same y-intercept? 50

51 Example: Now suppose the system of equations was instead a system of inequalities: How did the solution set change from the last example? What if we changed the problem to 3x + y 5 and 3x + y 8? Example: Where does the solution to the system of inequalities lie? What is true about all of the points in this region? 51

52 Example: 52

53 Module 1 Topic C Solving Equations and Inequalities Problem Set Lesson 22 - Systems of Equations (Graphing & Substitution) & Systems of Inequalities 1) Solve the following system of equations first by graphing and then algebraically. 3y 2x = 11 y + 2x = 9 2) 53

54 3) (Hint: It might be fun and easier to read if you used three different colored pencils to graph this system.) 4) a. b. c. 54

55 Module 1 Topic C Solving Equations and Inequalities Lesson 23 Systems of Equations (Addition/Elimination Method) REVIEW: Example: NEW: Example: Solve this system algebraically: Example: Solve this system algebraically: 55

56 Module 1 Topic C Solving Equations and Inequalities Lesson 23 - Systems of Equations (Addition/Elimination Method) Problem Set 1) Solve each system of equations by using the Addition/Elimination method. Include a check for each problem. 2) 3) 56

57 Module 1 Topic C Solving Equations and Inequalities Lesson 24 - Applications of Systems of Equations and Inequalities Example: Can we solve the problem above by only using Tweedledum s sentence? In a situation where there are two unknowns, how many equations do we need to write in order to solve the system? If I told you I was holding 20 coins that were some mix of dimes and quarters, could you tell me anything about how many of each I have? What other piece of information would be useful in determining how many of each type of coin I was holding? 57

58 Example: Example: 58

59 Example: 59

60 Module 1 Topic C Solving Equations and Inequalities Lesson 24 - Applications of Systems of Equations and Inequalities Problem Set 60

61 a. b. c. d. e. 61