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Geometry Section 0-5 1112

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J
Jimbo Lamb

The document provides an introduction to solving linear equations. It explains that to solve a linear equation, you must isolate the variable by doing the opposite operations of both sides of the equation. An example problem is worked through step-by-step, showing how to isolate the variable using addition, subtraction, multiplication, and division. The example checks the solution by substituting it back into the original equation. Students are then given a problem set to practice solving linear equations involving multiples of three.

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Section 0-5 Linear Equations Wednesday, September 14, 2011
Essential Question • How do you use Algebra to solve linear equations? Wednesday, September 14, 2011
Things to Remember Wednesday, September 14, 2011
Things to Remember • Isolate the variable Wednesday, September 14, 2011
Things to Remember • Isolate the variable • Do the opposite operations Wednesday, September 14, 2011
Things to Remember • Isolate the variable • Do the opposite operations • Check your answers Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 x =14 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 x =14 Check: Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Check: Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Check: 2(4) +12 = 20 Wednesday, September 14, 2011
Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Check: 2(4) +12 = 20 8 +12 = 20 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r d. − = 5 6 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 d. − = 5 6 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 Check: Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 Check: 5(25) =125 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 5(25) =125 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 r = −30 5(25) =125 Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 r = −30 5(25) =125 Check: Wednesday, September 14, 2011
Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 r = −30 5(25) =125 Check: −30 − =5 6 Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 2 h=8 3 Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 2 h=8 3 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 h=8 3 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 Check: h=8 3 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 Check: h=8 3 2 (12) + 9 =17 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ 3 h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 Check: h=8 3 2 (12) + 9 =17 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ 3 h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ 8 + 9 =17 Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −4m Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m 3 Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m 3 3 Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m 3 3 −5 = m Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 3 3 −5 = m Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 4(−5) − 3 = 7(−5) +12 3 3 −5 = m Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 4(−5) − 3 = 7(−5) +12 3 3 −20 − 3 = −35 +12 −5 = m Wednesday, September 14, 2011
Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 4(−5) − 3 = 7(−5) +12 3 3 −20 − 3 = −35 +12 −5 = m −23 = −23 Wednesday, September 14, 2011
Problem Set Wednesday, September 14, 2011
Problem Set p. P12 #1-36, multiples of 3 “When you make a mistake, there are only three things you should ever do about it: admit it, learns from it, and don’t repeat it.” - Paul “Bear” Bryant Wednesday, September 14, 2011

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Geometry Section 0-5 1112

  • 1. Section 0-5 Linear Equations Wednesday, September 14, 2011
  • 2. Essential Question • How do you use Algebra to solve linear equations? Wednesday, September 14, 2011
  • 3. Things to Remember Wednesday, September 14, 2011
  • 4. Things to Remember • Isolate the variable Wednesday, September 14, 2011
  • 5. Things to Remember • Isolate the variable • Do the opposite operations Wednesday, September 14, 2011
  • 6. Things to Remember • Isolate the variable • Do the opposite operations • Check your answers Wednesday, September 14, 2011
  • 7. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 Wednesday, September 14, 2011
  • 8. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 Wednesday, September 14, 2011
  • 9. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 Wednesday, September 14, 2011
  • 10. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 Wednesday, September 14, 2011
  • 11. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 x =14 Wednesday, September 14, 2011
  • 12. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 x =14 Check: Wednesday, September 14, 2011
  • 13. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 14. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 15. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 16. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 17. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 18. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 19. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: 14 −18 = −4 Wednesday, September 14, 2011
  • 20. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Wednesday, September 14, 2011
  • 21. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Check: Wednesday, September 14, 2011
  • 22. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Check: 2(4) +12 = 20 Wednesday, September 14, 2011
  • 23. Example 1 Solve. a. x −18 = −4 b. 2b +12 = 20 +18 +18 −12 −12 x =14 2b = 8 2 2 Check: b=4 14 −18 = −4 Check: 2(4) +12 = 20 8 +12 = 20 Wednesday, September 14, 2011
  • 24. Example 1 Solve. c. 5t =125 r d. − = 5 6 Wednesday, September 14, 2011
  • 25. Example 1 Solve. c. 5t =125 r 5 d. − = 5 6 Wednesday, September 14, 2011
  • 26. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 Wednesday, September 14, 2011
  • 27. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 Wednesday, September 14, 2011
  • 28. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 Check: Wednesday, September 14, 2011
  • 29. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 Check: 5(25) =125 Wednesday, September 14, 2011
  • 30. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 5(25) =125 Wednesday, September 14, 2011
  • 31. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 r = −30 5(25) =125 Wednesday, September 14, 2011
  • 32. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 r = −30 5(25) =125 Check: Wednesday, September 14, 2011
  • 33. Example 1 Solve. c. 5t =125 r 5 5 d. − = 5 6 t = 25 r (−6)(− ) = 5(−6) Check: 6 r = −30 5(25) =125 Check: −30 − =5 6 Wednesday, September 14, 2011
  • 34. Example 1 Solve. 2 e. h + 9 =17 3 Wednesday, September 14, 2011
  • 35. Example 1 Solve. 2 e. h + 9 =17 3 −9 Wednesday, September 14, 2011
  • 36. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 Wednesday, September 14, 2011
  • 37. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 Wednesday, September 14, 2011
  • 38. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 2 h=8 3 Wednesday, September 14, 2011
  • 39. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 2 h=8 3 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
  • 40. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 h=8 3 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
  • 41. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 Check: h=8 3 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
  • 42. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 Check: h=8 3 2 (12) + 9 =17 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ 3 h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ Wednesday, September 14, 2011
  • 43. Example 1 Solve. 2 e. h + 9 =17 3 −9 −9 h =12 2 Check: h=8 3 2 (12) + 9 =17 ⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ 3 h⎟ = 8 ⎜ ⎟ ⎜ 2⎟ ⎜ 3 ⎠ ⎝ ⎠⎝ ⎝ 2⎠ 8 + 9 =17 Wednesday, September 14, 2011
  • 44. Example 1 Solve. f. 4m − 3 = 7m +12 Wednesday, September 14, 2011
  • 45. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −4m Wednesday, September 14, 2011
  • 46. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Wednesday, September 14, 2011
  • 47. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m Wednesday, September 14, 2011
  • 48. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m 3 Wednesday, September 14, 2011
  • 49. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m 3 3 Wednesday, September 14, 2011
  • 50. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 −15 = 3m 3 3 −5 = m Wednesday, September 14, 2011
  • 51. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 3 3 −5 = m Wednesday, September 14, 2011
  • 52. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 4(−5) − 3 = 7(−5) +12 3 3 −5 = m Wednesday, September 14, 2011
  • 53. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 4(−5) − 3 = 7(−5) +12 3 3 −20 − 3 = −35 +12 −5 = m Wednesday, September 14, 2011
  • 54. Example 1 Solve. f. 4m − 3 = 7m +12 −4m −12 −4m −12 Check: −15 = 3m 4(−5) − 3 = 7(−5) +12 3 3 −20 − 3 = −35 +12 −5 = m −23 = −23 Wednesday, September 14, 2011
  • 56. Problem Set p. P12 #1-36, multiples of 3 “When you make a mistake, there are only three things you should ever do about it: admit it, learns from it, and don’t repeat it.” - Paul “Bear” Bryant Wednesday, September 14, 2011