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Tutorial

  1. 1. <ul><li>Tutorial: </li></ul><ul><li>Solving Multi-Step </li></ul><ul><li>Equations </li></ul>Click here to begin
  2. 2. <ul><li>By the end of this tutorial, you will be able to: </li></ul><ul><li>Define the terms equation , coefficient , constant , inverse operation , and variable </li></ul><ul><li>2. Solve a multi-step equation with one variable </li></ul>
  3. 3. <ul><li>Variable </li></ul><ul><li>A variable is a letter used to represent a missing or unknown number in an equation. </li></ul><ul><li>Example A: 2 x + 5 = 7 </li></ul><ul><li>Example B: -5 n – 20 = 5 </li></ul>variable variable
  4. 4. <ul><li>Equation </li></ul><ul><li>An equation is a statement formed by placing an equal sign between two expressions </li></ul><ul><li>Example A: 2 x + 5 = 7 </li></ul><ul><li>Example B: 4 x = 20 </li></ul><ul><li>Example C: </li></ul><ul><li>Non-Example A: 25n </li></ul><ul><li>Non-Example B: 2x 2 + 3x + 7 </li></ul>
  5. 5. <ul><li>Coefficient </li></ul><ul><li>A coefficient is the term that multiplies the variable in an expression or equation. </li></ul><ul><li>Example A: 2 x + 5 = 7 </li></ul><ul><li>Example B: -5 n – 20 = 5 </li></ul>coefficient coefficient
  6. 6. <ul><li>Constant </li></ul><ul><li>A constant is the term in an equation that stands alongside the variable and its coefficient. </li></ul><ul><li>Example A: 2 x + 5 = 7 </li></ul><ul><li>Example B: -5 n – 20 = 5 </li></ul>constant constant
  7. 7. <ul><li>Inverse Operation </li></ul><ul><li>An inverse operation is the opposite operation in an equation that allows isolation. </li></ul><ul><li>Example A: 2 x + 5 = 7 </li></ul><ul><li>Example B: 5 n = 5 </li></ul>Subtracting 5 is the inverse operation Dividing by 5 is the inverse operation
  8. 8. <ul><li>Practice: What you’ve learned </li></ul><ul><li>Now that we’ve gone over important vocabulary words, let’s see what you’ve learned. Click the appropriate letter to answer each question </li></ul><ul><li>1. Which of the following is an equation: </li></ul><ul><li>2n </li></ul><ul><li>2n + 7 </li></ul><ul><li>2n + 7 = 15 </li></ul><ul><li>None of these </li></ul>A B D C
  9. 9. <ul><li>Practice: What you’ve learned </li></ul><ul><li>Now that we’ve gone over important vocabulary words, let’s see what you’ve learned. Click the appropriate letter to answer each question </li></ul><ul><li>1. Which of the following is an equation: </li></ul><ul><li>2n </li></ul><ul><li>2n + 7 </li></ul><ul><li>2n + 7 = 15 </li></ul><ul><li>None of these </li></ul>A B D C This is an expression. Click here to go back and try again.
  10. 10. <ul><li>Practice: What you’ve learned </li></ul><ul><li>Now that we’ve gone over important vocabulary words, let’s see what you’ve learned. Click the appropriate letter to answer each question </li></ul><ul><li>1. Which of the following is an equation: </li></ul><ul><li>2n </li></ul><ul><li>2n + 7 </li></ul><ul><li>2n + 7 = 15 </li></ul><ul><li>None of these </li></ul>A B D C This is an expression. Click here to go back and try again
  11. 11. <ul><li>Practice: What you’ve learned </li></ul><ul><li>Now that we’ve gone over important vocabulary words, let’s see what you’ve learned. Click the appropriate letter to answer each question </li></ul><ul><li>1. Which of the following is an equation: </li></ul><ul><li>2n </li></ul><ul><li>2n + 7 </li></ul><ul><li>2n + 7 = 15 </li></ul><ul><li>None of these </li></ul>A B D C Correct! Next Question
  12. 12. <ul><li>Practice: What you’ve learned </li></ul><ul><li>Now that we’ve gone over important vocabulary words, let’s see what you’ve learned. Click the appropriate letter to answer each question </li></ul><ul><li>1. Which of the following is an equation: </li></ul><ul><li>2n </li></ul><ul><li>2n + 7 </li></ul><ul><li>2n + 7 = 15 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  13. 13. <ul><li>2. A variable is a letter that represents: </li></ul><ul><li>a number </li></ul><ul><li>a fraction </li></ul><ul><li>an unknown number </li></ul><ul><li>None of these </li></ul>A B D C
  14. 14. <ul><li>2. A variable is a letter that represents: </li></ul><ul><li>a number </li></ul><ul><li>a fraction </li></ul><ul><li>an unknown number </li></ul><ul><li>None of these </li></ul>A B D C Not just a number. Click here to go back and try again
  15. 15. <ul><li>2. A variable is a letter that represents: </li></ul><ul><li>a number </li></ul><ul><li>a fraction </li></ul><ul><li>an unknown number </li></ul><ul><li>None of these </li></ul>A B D C It can be a fraction, but be more specific. Click here to go back and try again
  16. 16. <ul><li>2. A variable is a letter that represents: </li></ul><ul><li>a number </li></ul><ul><li>a fraction </li></ul><ul><li>an unknown number </li></ul><ul><li>None of these </li></ul>A B D C Correct! Next Question
  17. 17. <ul><li>2. A variable is a letter that represents: </li></ul><ul><li>a number </li></ul><ul><li>a fraction </li></ul><ul><li>an unknown number </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  18. 18. <ul><li>3. What is the inverse operation of + 7: </li></ul><ul><li>divide by 7 </li></ul><ul><li>subtract 7 </li></ul><ul><li>multiply by 7 </li></ul><ul><li>None of these </li></ul>A B D C
  19. 19. <ul><li>3. What is the inverse operation of + 7: </li></ul><ul><li>divide by 7 </li></ul><ul><li>subtract 7 </li></ul><ul><li>multiply by 7 </li></ul><ul><li>None of these </li></ul>A B D C An inverse operation is the opposite operation. Click here to go back and try again
  20. 20. <ul><li>3. What is the inverse operation of + 7: </li></ul><ul><li>divide by 7 </li></ul><ul><li>subtract 7 </li></ul><ul><li>multiply by 7 </li></ul><ul><li>None of these </li></ul>A B D C Correct Next Question
  21. 21. <ul><li>3. What is the inverse operation of + 7: </li></ul><ul><li>divide by 7 </li></ul><ul><li>subtract 7 </li></ul><ul><li>multiply by 7 </li></ul><ul><li>None of these </li></ul>A B D C An inverse operation is the opposite operation. Click here to go back and try again
  22. 22. <ul><li>3. What is the inverse operation of + 7: </li></ul><ul><li>divide by 7 </li></ul><ul><li>subtract 7 </li></ul><ul><li>multiply by 7 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  23. 23. <ul><li>4. Identify the coefficient in the equation 3n – 12 = 80: </li></ul><ul><li>3 </li></ul><ul><li>n </li></ul><ul><li>12 </li></ul><ul><li>None of these </li></ul>A B D C
  24. 24. <ul><li>4. Identify the coefficient in the equation 3n – 12 = 80: </li></ul><ul><li>3 </li></ul><ul><li>n </li></ul><ul><li>12 </li></ul><ul><li>None of these </li></ul>A B D C Correct Continue Tutorial
  25. 25. <ul><li>4. Identify the coefficient in the equation 3n – 12 = 80: </li></ul><ul><li>3 </li></ul><ul><li>n </li></ul><ul><li>12 </li></ul><ul><li>None of these </li></ul>A B D C This is a variable. Click here to go back and try again.
  26. 26. <ul><li>4. Identify the coefficient in the equation 3n – 12 = 80: </li></ul><ul><li>3 </li></ul><ul><li>n </li></ul><ul><li>12 </li></ul><ul><li>None of these </li></ul>A B D C This is the constant. Click here to go back and try again
  27. 27. <ul><li>4. Identify the coefficient in the equation 3n – 12 = 80: </li></ul><ul><li>3 </li></ul><ul><li>n </li></ul><ul><li>12 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  28. 28. <ul><li>How to solve a multi-step equation with one variable </li></ul><ul><li>We will now go through the step-by-step procedure in solving a multi-step equation using the example 2x + 7 = 15 </li></ul>
  29. 29. <ul><li>2x + 7 = 15 </li></ul><ul><li>- 7 - 7 </li></ul><ul><li>First, eliminate the constant by finding its inverse operation . The equation needs to be balanced so if you subtract 7 on one side of the equal sign, you must do the same on the other side of the equal sign. </li></ul>
  30. 30. <ul><li>2x + 7 = 15 </li></ul><ul><li>- 7 - 7 </li></ul><ul><li> 2x = 8 </li></ul><ul><li>+7 and -7 cancel out and you are left with the equation 2x = 8 </li></ul>
  31. 31. <ul><li>2x = 8 </li></ul><ul><li>2 2 </li></ul><ul><li>From here you must isolate x by eliminating the coefficient of 2 through its inverse operation. Once again, the equation needs to be balanced. If you divide by 2 on one side of the equal sign, you must do the same on the other side of the equal sign. </li></ul>
  32. 32. <ul><li>2x = 8 </li></ul><ul><li>2 2 </li></ul><ul><li>The 2’s on the left side of the equation cancel out which isolates x and leaves or </li></ul><ul><li>8 ÷ 2, resulting in x = 4 </li></ul><ul><li>. </li></ul>
  33. 33. <ul><li>Congratulations! </li></ul><ul><li>You have just completed this tutorial. You should now have the confidence to solve a multi-step equation. </li></ul><ul><li>Click to take the quiz. </li></ul>here
  34. 34. <ul><li>1. What is the term that stands alongside the variable and coefficient? </li></ul><ul><li>the inverse operation </li></ul><ul><li>a fraction </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C
  35. 35. <ul><li>1. What is the term that stands alongside the variable and coefficient? </li></ul><ul><li>the inverse operation </li></ul><ul><li>a fraction </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C This is the opposite operation within the equation. Click here to go back and try again
  36. 36. <ul><li>1. What is the term that stands alongside the variable and coefficient? </li></ul><ul><li>the inverse operation </li></ul><ul><li>a fraction </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C It can be a fraction, but be more specific. Click here to go back and try again
  37. 37. <ul><li>1. What is the term that stands alongside the variable and coefficient? </li></ul><ul><li>the inverse operation </li></ul><ul><li>a fraction </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for the next question
  38. 38. <ul><li>1. What is the term that stands alongside the variable and coefficient? </li></ul><ul><li>the inverse operation </li></ul><ul><li>a fraction </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  39. 39. <ul><li>2. What is the term that multiplies the variable? </li></ul><ul><li>the equation </li></ul><ul><li>the coefficient </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C
  40. 40. <ul><li>2. What is the term that multiplies the variable? </li></ul><ul><li>the equation </li></ul><ul><li>the coefficient </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C This is an expression set equal to a solution.Click here to go back and try again
  41. 41. <ul><li>2. What is the term that multiplies the variable? </li></ul><ul><li>the equation </li></ul><ul><li>the coefficient </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for the next question
  42. 42. <ul><li>2. What is the term that multiplies the variable? </li></ul><ul><li>the equation </li></ul><ul><li>the coefficient </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C This is the term that stands alongside the variable and coefficient. Click here to go back and try again
  43. 43. <ul><li>2. What is the term that multiplies the variable? </li></ul><ul><li>the equation </li></ul><ul><li>the coefficient </li></ul><ul><li>the constant </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  44. 44. <ul><li>3. What is the unknown number in any equation? </li></ul><ul><li>the variable </li></ul><ul><li>the constant </li></ul><ul><li>the coefficient </li></ul><ul><li>None of these </li></ul>A B D C
  45. 45. <ul><li>3. What is the unknown number in any equation? </li></ul><ul><li>the variable </li></ul><ul><li>the constant </li></ul><ul><li>the coefficient </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for the next question
  46. 46. <ul><li>3. What is the unknown number in any equation? </li></ul><ul><li>the variable </li></ul><ul><li>the constant </li></ul><ul><li>the coefficient </li></ul><ul><li>None of these </li></ul>A B D C This is the term that stands alongside the variable and coefficient. Click here to go back and try again
  47. 47. <ul><li>3. What is the unknown number in any equation? </li></ul><ul><li>the variable </li></ul><ul><li>the constant </li></ul><ul><li>the coefficient </li></ul><ul><li>None of these </li></ul>A B D C This is the term that multiplies the variable. Click here to go back and try again
  48. 48. <ul><li>3. What is the unknown number in any equation? </li></ul><ul><li>the variable </li></ul><ul><li>the constant </li></ul><ul><li>the coefficient </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  49. 49. <ul><li>4. What is the first step in solving the equation: 2y + 5 = 1 </li></ul><ul><li>eliminate the coefficient </li></ul><ul><li>2 through division </li></ul><ul><li>eliminate 1 through </li></ul><ul><li>its inverse operation </li></ul><ul><li>eliminate the constant 5 </li></ul><ul><li>through its inverse operation </li></ul><ul><li>guess and check by </li></ul><ul><li>plugging in values for x </li></ul>A B D C
  50. 50. <ul><li>4. What is the first step in solving the equation: 2y + 5 = 1 </li></ul><ul><li>eliminate the coefficient </li></ul><ul><li>2 through division </li></ul><ul><li>eliminate 1 through </li></ul><ul><li>its inverse operation </li></ul><ul><li>eliminate the constant 5 </li></ul><ul><li>through its inverse operation </li></ul><ul><li>guess and check by </li></ul><ul><li>plugging in values for x </li></ul>A B D C This is the following step. Click here to go back and try again
  51. 51. <ul><li>4. What is the first step in solving the equation: 2y + 5 = 1 </li></ul><ul><li>eliminate the coefficient </li></ul><ul><li>2 through division </li></ul><ul><li>eliminate 1 through </li></ul><ul><li>its inverse operation </li></ul><ul><li>eliminate the constant 5 </li></ul><ul><li>through its inverse operation </li></ul><ul><li>guess and check by </li></ul><ul><li>plugging in values for x </li></ul>A B D C Eliminating 1 would make the equation unbalanced. Click here to go back and try again
  52. 52. <ul><li>4. What is the first step in solving the equation: 2y + 5 = 1 </li></ul><ul><li>eliminate the coefficient </li></ul><ul><li>2 through division </li></ul><ul><li>eliminate 1 through </li></ul><ul><li>its inverse operation </li></ul><ul><li>eliminate the constant 5 </li></ul><ul><li>through its inverse operation </li></ul><ul><li>guess and check by </li></ul><ul><li>plugging in values for x </li></ul>A B D C Correct! Click here for the next question.
  53. 53. <ul><li>4. What is the first step in solving the equation: 2y + 5 = 1 </li></ul><ul><li>eliminate the coefficient </li></ul><ul><li>2 through division </li></ul><ul><li>eliminate 1 through </li></ul><ul><li>its inverse operation </li></ul><ul><li>eliminate the constant 5 </li></ul><ul><li>through its inverse operation </li></ul><ul><li>guess and check by </li></ul><ul><li>plugging in values for x </li></ul>A B D C You can do this, but it may take a long period of time. Click here to go back and try again
  54. 54. <ul><li>5. Solve for the variable: 3g – 1 = 8 </li></ul><ul><li>3g = 6 </li></ul><ul><li>g = 3 </li></ul><ul><li>g = 9/3 </li></ul><ul><li>None of these </li></ul>A B D C
  55. 55. <ul><li>5. Solve for the variable: 3g – 1 = 8 </li></ul><ul><li>3g = 6 </li></ul><ul><li>g = 3 </li></ul><ul><li>g = 9/3 </li></ul><ul><li>None of these </li></ul>A B D C The variable g must be isolated Click here to go back and try again
  56. 56. <ul><li>5. Solve for the variable: 3g – 1 = 8 </li></ul><ul><li>3g = 6 </li></ul><ul><li>g = 3 </li></ul><ul><li>g = 9/3 </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for the next question.
  57. 57. <ul><li>5. Solve for the variable: 3g – 1 = 8 </li></ul><ul><li>3g = 6 </li></ul><ul><li>g = 3 </li></ul><ul><li>g = 9/3 </li></ul><ul><li>None of these </li></ul>A B D C You’re almost there. 9/3 must be simplified. Click here to go back and try again
  58. 58. <ul><li>5. Solve for the variable: 3g – 1 = 8 </li></ul><ul><li>3g = 6 </li></ul><ul><li>g = 3 </li></ul><ul><li>g = 9/3 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  59. 59. <ul><li>6. Solve for the variable: 2x + 5 = 15 </li></ul><ul><li>x = 10/2 </li></ul><ul><li>x = -5 </li></ul><ul><li>x = 5 </li></ul><ul><li>None of these </li></ul>A B D C
  60. 60. <ul><li>6. Solve for the variable: 2x + 5 = 15 </li></ul><ul><li>x = 10/2 </li></ul><ul><li>x = -5 </li></ul><ul><li>x = 5 </li></ul><ul><li>None of these </li></ul>A B D C You’re almost there. 10/2 must be simplified. Click here to go back and try again
  61. 61. <ul><li>6. Solve for the variable: 2x + 5 = 15 </li></ul><ul><li>x = 10/2 </li></ul><ul><li>x = -5 </li></ul><ul><li>x = 5 </li></ul><ul><li>None of these </li></ul>A B D C Not quite. The solution is opposite in sign. Click here to go back and try again
  62. 62. <ul><li>6. Solve for the variable: 2x + 5 = 15 </li></ul><ul><li>x = 10/2 </li></ul><ul><li>x = -5 </li></ul><ul><li>x = 5 </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for the next question
  63. 63. <ul><li>6. Solve for the variable: 2x + 5 = 15 </li></ul><ul><li>x = 10/2 </li></ul><ul><li>x = -5 </li></ul><ul><li>x = 5 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  64. 64. <ul><li>7. Solve for the variable: 3y + 5 = 11 </li></ul><ul><li>y = 2 </li></ul><ul><li>3y = 6 </li></ul><ul><li>y = 6/3 </li></ul><ul><li>None of these </li></ul>A B D C
  65. 65. <ul><li>7. Solve for the variable: 3y + 5 = 11 </li></ul><ul><li>y = 2 </li></ul><ul><li>3y = 6 </li></ul><ul><li>y = 6/3 </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for the next question
  66. 66. <ul><li>7. Solve for the variable: 3y + 5 = 11 </li></ul><ul><li>y = 2 </li></ul><ul><li>3y = 6 </li></ul><ul><li>y = 6/3 </li></ul><ul><li>None of these </li></ul>A B D C You need to isolate the variable y. Click here to go back and try again
  67. 67. <ul><li>7. Solve for the variable: 3y + 5 = 11 </li></ul><ul><li>y = 2 </li></ul><ul><li>3y = 6 </li></ul><ul><li>y = 6/3 </li></ul><ul><li>None of these </li></ul>A B D C You’re almost there. 6/3 must be simplified. Click here to go back and try again
  68. 68. <ul><li>7. Solve for the variable: 3y + 5 = 11 </li></ul><ul><li>y = 2 </li></ul><ul><li>3y = 6 </li></ul><ul><li>y = 6/3 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  69. 69. <ul><li>8. Solve for the variable: 7t – 9 = 19 </li></ul><ul><li>t = -28 </li></ul><ul><li>t = 4 </li></ul><ul><li>t = 28/7 </li></ul><ul><li>None of these </li></ul>A B D C
  70. 70. <ul><li>8. Solve for the variable: 7t – 9 = 19 </li></ul><ul><li>t = -28 </li></ul><ul><li>t = 4 </li></ul><ul><li>t = 28/7 </li></ul><ul><li>None of these </li></ul>A B D C Check your calculations. Click here to go back and try again
  71. 71. <ul><li>8. Solve for the variable: 7t – 9 = 19 </li></ul><ul><li>t = -28 </li></ul><ul><li>t = 4 </li></ul><ul><li>t = 28/7 </li></ul><ul><li>None of these </li></ul>A B D C Correct! Click here for results.
  72. 72. <ul><li>8. Solve for the variable: 7t – 9 = 19 </li></ul><ul><li>t = -28 </li></ul><ul><li>t = 4 </li></ul><ul><li>t = 28/7 </li></ul><ul><li>None of these </li></ul>A B D C You’re almost there. 28/7 must be simplified. Click here to go back and try again
  73. 73. <ul><li>8. Solve for the variable: 7t – 9 = 19 </li></ul><ul><li>t = -28 </li></ul><ul><li>t = 4 </li></ul><ul><li>t = 28/7 </li></ul><ul><li>None of these </li></ul>A B D C Click here to go back and try again
  74. 74. <ul><li>Find your percentage by dividing the total correct by the total number of questions. </li></ul>8/8 = A+ 6/8 = C 5/8 = D 7/8 = B 4/8 & Below = F

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