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Chapter 2

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Chapter 2

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  1. Chapter 2 Solving Equations

  2. Students will be able to solve one step equations using addition and subtraction.

  3. Linear Equations The variable(s) in the equation is(are) to the first power. Examples that are not linear equations: Examples:

  4. Equations An equation shows that two quantities are equal “Keep the equation balanced”

  5. Solving Equations To solve an equation: isolate the variable,thatis get the variable ALONE on one side of the equal sign. use inverse operations. Inverse operations are operations which undo each other

  6. Solving Equations: OperationInverse Operation Addition Subtraction Addition Subtraction Division Multiplication Multiplication Division

  7. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  8. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  9. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  10. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? – 15 – 15 What you do on one side of the equal sign, you must do on the other!

  11. Examples:

  12. Solving one-step equations Section 2.1

  13. Students will be able to solve one-step algebraic equations using multiplication and division.

  14. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  15. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  16. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  17. Solving: How do you isolate the variable? What is happening to it and how can you “undo” this? What you do on one side of the equal sign, you must do on the other!

  18. Solving: Multiply by the reciprocal to “undo” a fraction

  19. Solving: Multiply by the reciprocal to “undo” a fraction

  20. Examples:

  21. 2.1 Word Problems On January 22, 1943, the temperature in Spearfish fell from 54ºF at 9:00 A.M. To -4ºF at 9:27 A.M. How many degrees did the temperature fall. Define the variable: 2) Write your equation: 3) Solve your equation: 4) Answer in a complete sentence x = temperature fall 54 – x = - 4 -54 -54 – x = – 60 x = 60 The temperature dropped 60º

  22. 2.1 Word Problem The following triangle has a perimeter of 40 cm. What is the length of the unknown side? Define the variable: Write your equation: Solve your equation: 4) Answer in a complete sentence. x 8 cm 12 cm

  23. 2.1 Word Problems Helen is planning to go to the grocery store and buy eggs for her bagel shop. If each carton of eggs contains 12 eggs, how many cartons must she buy to obtain 450 eggs? a) x = # of cartons b) 12x = 450 12 12 c) x = 37.5 cartons or d) 38 whole cartons

  24. 2.1 Word Problems You are working on a banner for Saturday’s field hockey game. The length of the banner is 4 times the width. The length is 12 feet. What is the width? • Define the variable • Write an equation • Solve the equation • Write answer in complete sentence Go Glastonbury

  25. 2.1 Word Problems Jason’s mom is going to take him and a few friends to see the new Harry Potter movie Friday night. She has $60 and each ticket costs $12. How many people can go to the movie? If mom wants to go also, how many friends can Jason invite? 1) Define the variable 2) Write an equation 3) Solve the equation 4) Write answer in complete sentence Don’t forget to bring your teacher

  26. 2.1 Word Problems You purchase a cane of polymer clay to make pendants for necklaces. The cane is 50 millimeters long. How thick should you make each pendant so that you will have 20 pendants of uniform thickness? • Define the variable • Write an equation • Solve the equation • Write answer in complete sentence

  27. Solving Two-Step Equations Section 2.2

  28. Students will be able to solve two-step equations in one variable.

  29. Solving Multi-Step Equations: Isolate the variable term. Isolate the variable.

  30. Solving Multi-Step Equations: Isolate the variable term. Isolate the variable.

  31. Solving Multi-Step Equations: Isolate the variable term. Isolate the variable.

  32. Solving Multi-Step Equations:

  33. Solving Multi-Step Equations:

  34. Examples: 1) 2) 3) 4)

  35. Section 2.2 continued Students will be able to solve two-step equations in one variable.

  36. Two step problems Isolate the variable term. (5) (5) Isolate the variable. 46

  37. Two step problems Isolate the variable term. 8 (-2) (-2) Isolate the variable. -16 6 -10

  38. You try!!

  39. Two step word problems 1) 331 students were supposed to go on a field trip. They filled six buses, and 7 students did not go because they were sick. How many students were in each bus? Define the variable: x = # of students 6x + 7 = 331 Write an equation: 6x = 324 Solve the equation: x = 54 There is 54 students per bus Answer in a sentence:

  40. Two step word problems 2) Leah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost? p = cost of pencils Define the variable: 24 – 7p = 10 Write an equation: -7p = -14 Solve the equation: p = 2 Answer in a sentence: Each pencil cost $2.00

  41. Two step word problems 3) You spent $25 on a magazine and 4 binders. The magazine was $5. How much did each binder cost? c = cost of each binder Define the variable: 4c + 5 = 25 Write an equation: 4c = 20 Solve the equation: c = 5 Answer in a sentence: Each binder cost $5.00

  42. Solving Multi-Step Equation Section 2.3 Part 1

  43. Students will be able to solve multi-step equations in one variable

  44. Combine Like Terms Isolate variable term Isolate variable

  45. Combine Like Terms Isolate variable term Isolate variable 9

  46. What should I do first?

  47. 4 7

  48. Examples:

  49. Examples:

  50. YOU TRY: 1) 2) 3) 4)