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by Anjie Julseth31 views·Updated Oct 23, 2020
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  1. Hi guys.
  2. Miss Joel.
  3. Seth Here and today we're going to talk about solving
  4. multi stuff Equations.
  5. Solving multi step equations means we use two or more
  6. transformations to solve an equation.
  7. Remember that solving an equation is a balancing act.
  8. What you do to one side, you have to do
  9. to the other.
  10. Okay, steps for solving.
  11. First we simplify one or both sides of the equation.
  12. If that's needed, then we use in inverse operations toe
  13. isolate the variables so we do the opposite of the
  14. order of operations.
  15. Okay, So to simplify, you use PEM dust and to
  16. solve you do the opposite, which is sad map.
  17. Okay, Solving a linear equation.
  18. We have one third X plus six equals negative eight.
  19. First, we need to get rid of what's being added.
  20. So the positive six and it becomes negative six because
  21. you do the opposite.
  22. So we have one third x equals negative 14 because
  23. negative eight and negative six is negative 14.
  24. Then, to get rid of the fraction we multiply by
  25. the reciprocal.
  26. So this reciprocal of 1/3 is just 3/1.
  27. You just flip the fraction.
  28. So we have three times one third x equals negative
  29. 14 times three.
  30. Look, we did the same thing to both sides three
  31. times. One third just gets rid of that fraction completely
  32. because it becomes 3/3, which is just one.
  33. So we have X equals negative 42 because negative 14
  34. times three is negative.
  35. 42. Okay, now, this is a problem where we would
  36. combine like terms first.
  37. So we have seven X minus three X minus eight
  38. equals 24 and seven X minus three X is for
  39. X minus eight equals 24.
  40. Now we get rid of the negative eight by adding
  41. eight to both sides.
  42. So we have four x equals 24 plus eight is
  43. 30 to divide both sides by four and we get
  44. X equals eight.
  45. Okay, here we use the distributive property.
  46. So we have five x plus three times the quantity
  47. X plus four equals 28.
  48. So when you distribute the three you get five x
  49. plus three times X is three x plus three times
  50. four is 12 equals 28 5 x plus three x
  51. is eight x plus 12 equals 28.
  52. Subtract 12 from both sides we get eight X equals
  53. 16 divide both sides by eight and we get X
  54. equals two.
  55. Okay, now we have distributed getting in an excuse me
  56. distributing and negative.
  57. Okay, so we have four X minus three times the
  58. quantity X minus two equals 21.
  59. So that minus three is the same as plus a
  60. negative three.
  61. So we're really distributing and negative three.
  62. We have four x negative.
  63. Three times X is negative three x and negative.
  64. Three times negative two is positive.
  65. Six equals 21.
  66. Then we combine the like terms on the left.
  67. So four X one is three.
  68. X s one X plus six equals 21.
  69. We subtract six from both sides and we get X
  70. equals 15.
  71. Okay. Now multiplying by a reciprocal first on that other
  72. one. We had to get rid of the six first
  73. and then multiply by the reciprocal.
  74. But because the fraction is outside of the parentheses, you
  75. multiply by the reciprocal first.
  76. Okay, so that means we're gonna multiplied by negative 5/6.
  77. Because the reciprocal of 6/5 is 5/6 and we still
  78. need to keep the negative and remember that fractions.
  79. Air division.
  80. So really, you can cross cancel you could go 66
  81. divided by six, which is 11 and then 11 times
  82. negative. Five is negative 55 and multiplying by the reciprocal
  83. on the right side gets rid of the fraction completely.
  84. So you're just left with what's inside of the parentheses,
  85. which is X plus three.
  86. Okay, then to get X by itself, we subtract three
  87. from both sides.
  88. Negative 55 minus three is negative.
  89. 58. So X equals negative.
  90. 58 cross multiplying the entire group and then distributing.
  91. So when we have five over the quantity X minus
  92. three equals four over the quantity X plus two, that
  93. entire quantity has to multiply from the bottom across the
  94. equals to the top, and same with on the right
  95. side, from the bottom, across the equals to the top.
  96. So we do five times the quantity X plus two,
  97. which was underneath the four, and then four times the
  98. quantity X minus three, which was underneath the five.
  99. Okay, so we distribute the five, we get five X
  100. plus 10 we distribute the four.
  101. We get four X minus three.
  102. Now we combine like terms.
  103. We have to move the four X to the left
  104. side by subtracting it and move the 10 to the
  105. right side by subtracting it So five X minus four
  106. X is one X and negative 12 and negative.
  107. 10 is negative.
  108. 22. So there we have it.
  109. Solid multi step equations.
  110. You know, you can always pause the video and right
  111. thes examples down in your notes.
  112. I highly recommend that Have a great day.