Algebra 1 lessonplan powerpoint

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Algebra 1 lessonplan powerpoint

  1. 1. Algebra 1
  2. 2. Solving Equations withVariables on BOTH sides
  3. 3. Solving Equations withVariables on BOTH sides Variable: In algebra the variables are letters used to hold the place of a missing number in an equation. Most commonly used variables are ‘x’ and ‘y’ Any letter may be used to hold the place of the missing number in the equation.
  4. 4. Solving Equations withVariables on BOTH sides Variable: In algebra the variables are letters used to hold the place of a missing number in an equation. Most commonly used variables are ‘x’ and ‘y’ Any letter may be used to hold the place of the missing number in the equation. Our goal today: To solve an equation that has a variable on BOTH sides of the equation.
  5. 5. REVIEW: 6X+4=28
  6. 6. REVIEW: 6X+4=28Solve this equation:6x+4=28
  7. 7. REVIEW: 6X+4=28Solve this equation:6x+4=28Subtract the 4 from both sides of the equation6x+4=28 -4 -46x =24
  8. 8. REVIEW: 6X+4=28Solve this equation:6x+4=28Subtract the 4 from both sides of the equation6x+4=28 -4 -46x =24Now divide each side by 66x = 246 6We now have gotten ‘x’ by itself and solved the equation x=4
  9. 9. Taking the Next Step::
  10. 10. Taking the Next Step::What does an equation with 2 variables look like??
  11. 11. Taking the Next Step::What does an equation with 2 variables look like??Examples:4x+13=12x+45 3x+8=2x+105x+7=9x-5 9x-17=3x-23
  12. 12. Step by Step we solve the equation:
  13. 13. Step by Step we solve the equation: Step 1: Combining like terms and rearranging the equation so we can easily solve the problem. First we move the numbers which have no variable attached to them.
  14. 14. Step by Step we solve the equation: Step 1: Combining like terms and rearranging the equation so we can easily solve the problem. First we move the numbers which have no variable attached to them. Step 2: Move the numbers WITH variables attached to them
  15. 15. Step by Step we solve the equation: Step 1: Combining like terms and rearranging the equation so we can easily solve the problem. First we move the numbers which have no variable attached to them. Step 2: Move the numbers WITH variables attached to them Step 3: Divide each side of the equation by the number attached to the variable
  16. 16. Step 1: Moving the Number without theVariable
  17. 17. Step 1: Moving the Number without theVariable4x+13=12x+45 3x+8=2x+105x+7=9x-5 9x-17=3x-23
  18. 18. Step 1: Moving the Number without theVariable4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -85x+7=9x-5 9x-17=3x-23 +5 +5 +23 +23
  19. 19. Step 1: Moving the Number without theVariable4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -84x =12x+32 3x =2x+25x+7=9x-5 9x-17=3x-23 +5 +5 +23 +235x+12=9x 9x+6=3x
  20. 20. Step 2: Moving the number WITH thevariable
  21. 21. Step 2: Moving the number WITH thevariable 4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -8 4x =12x+32 3x =2x+2 -12x -12x -2x -2x _ 5x+7=9x-5 9x-17=3x-23 +5 +5 +23 +23 5x+12=9x 9x+6=3x -5x -5x -9x -9x _
  22. 22. Step 2: Moving the number WITH thevariable 4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -8 4x =12x+32 3x =2x+2 -12x -12x -2x -2x _ -8x = 32 1x = 2 5x+7=9x-5 9x-17=3x-23 +5 +5 +23 +23 5x+12=9x 9x+6=3x -5x -5x -9x -9x _ 12= 4x 6 = -6x
  23. 23. Step 3: Dividing each side by the numberattached to the variable4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -84x =12x+32 3x =2x+2-12x -12x -2x -2x _-8x = 32 1x = 2-8 -8 1 15x+7=9x-5 9x-17=3x-23 +5 +5 +23 +235x+12=9x 9x+6=3x-5x -5x -9x -9x _ 12= 4x 6 = -6x 4 4 -6 -6
  24. 24. SOLUTIONS
  25. 25. SOLUTIONS4x+13=12x+45 -13 -134x =12x+32-12x -12x _-8x = 32-8 -8Solution x= -4
  26. 26. SOLUTIONS4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -84x =12x+32 3x =2x+2-12x -12x -2x -2x _-8x = 32 1x = 2-8 -8 1 1Solution x= -4 Solution x=2
  27. 27. SOLUTIONS4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -84x =12x+32 3x =2x+2-12x -12x -2x -2x _-8x = 32 1x = 2-8 -8 1 1Solution x= -4 Solution x=25x+7=9x-5 +5 +55x+12=9x-5x -5x 12= 4x 4 4Solution x=3
  28. 28. SOLUTIONS4x+13=12x+45 3x+8=2x+10 -13 -13 -8 -84x =12x+32 3x =2x+2-12x -12x -2x -2x _-8x = 32 1x = 2-8 -8 1 1Solution x= -4 Solution x=25x+7=9x-5 9x-17=3x-23 +5 +5 +23 +235x+12=9x 9x+6=3x-5x -5x -9x -9x _ 12= 4x 6 = -6x 4 4 -6 -6Solution x=3 Solution x= -1
  29. 29. Check your work!!
  30. 30. Check your work!! Plug the solution into the original problem
  31. 31. Check your work!! Plug the solution into the original problemLet’s check our solution for example problem #1
  32. 32. Check your work!! Plug the solution into the original problemLet’s check our solution for example problem #1 4x+13=12x+45 where x= -4
  33. 33. Check your work!! Plug the solution into the original problemLet’s check our solution for example problem #1 4x+13=12x+45 where x= -4 4(-4)+13 = 12(-4)+45
  34. 34. Check your work!! Plug the solution into the original problemLet’s check our solution for example problem #1 4x+13=12x+45 where x= -4 4(-4)+13 = 12(-4)+45 -16 + 13 = -48 + 45
  35. 35. Check your work!! Plug the solution into the original problemLet’s check our solution for example problem #1 4x+13=12x+45 where x= -4 4(-4)+13 = 12(-4)+45 -16 + 13 = -48 + 45 -3 = -3
  36. 36. Checking our solution for example problem #2
  37. 37. Checking our solution for example problem #2 3x+8=2x+10 where x=2
  38. 38. Checking our solution for example problem #2 3x+8=2x+10 where x=2 3(2)+8=2(2)+10
  39. 39. Checking our solution for example problem #2 3x+8=2x+10 where x=2 3(2)+8=2(2)+10 6 +8= 4 +10
  40. 40. Checking our solution for example problem #2 3x+8=2x+10 where x=2 3(2)+8=2(2)+10 6 +8= 4 +10 14 = 14
  41. 41. Checking our solution for example problem #3
  42. 42. Checking our solution for example problem #3 5x+7=9x-5 where x=3
  43. 43. Checking our solution for example problem #3 5x+7=9x-5 where x=3 5(3)+7=9(3)-5
  44. 44. Checking our solution for example problem #3 5x+7=9x-5 where x=3 5(3)+7=9(3)-5 15 +7= 27 -5
  45. 45. Checking our solution for example problem #3 5x+7=9x-5 where x=3 5(3)+7=9(3)-5 15 +7= 27 -5 22 = 22
  46. 46. Checking our solution for example problem #4
  47. 47. Checking our solution for example problem #49x-17=3x-23 where x= -1
  48. 48. Checking our solution for example problem #49x-17=3x-23 where x= -19(-1)-17=3(-1)-23
  49. 49. Checking our solution for example problem #49x-17=3x-23 where x= -19(-1)-17=3(-1)-23 -9 -17= -3 -23
  50. 50. Checking our solution for example problem #49x-17=3x-23 where x= -19(-1)-17=3(-1)-23 -9 -17= -3 -23 -26 = -26
  51. 51. Your turn
  52. 52. Your turnSolve the equation: 3x+4=13x-6
  53. 53. Your turnSolve the equation: 3x+4=13x-61.Rearrange the equation 10x=10x
  54. 54. Your turnSolve the equation: 3x+4=13x-61.Rearrange the equation 10x=10x2.Divide by 10 x=1
  55. 55. Your turnSolve the equation: 3x+4=13x-61.Rearrange the equation 10x=10x2.Divide by 10 x=13.Check your solution 3+4=13-6
  56. 56. Your turnSolve the equation: 3x+4=13x-61.Rearrange the equation 10x=10x2.Divide by 10 x=13.Check your solution 3+4=13-6 7 = 7
  57. 57. Your turnSolve the equation: 3x+4=13x-61.Rearrange the equation 10x=10x2.Divide by 10 x=13.Check your solution 3+4=13-6 7 = 7 
  58. 58. Work for the problem 3x+4=13x-6
  59. 59. Work for the problem 3x+4=13x-63x+4=13x-6 +6 +6
  60. 60. Work for the problem 3x+4=13x-63x+4=13x-6 +6 +63x+10=13x
  61. 61. Work for the problem 3x+4=13x-6 3x+4=13x-6 +6 +6 3x+10=13x-3x -3x
  62. 62. Work for the problem 3x+4=13x-6 3x+4=13x-6 +6 +6 3x+10=13x-3x -3x 10=10x 10 10
  63. 63. Work for the problem 3x+4=13x-6 3x+4=13x-6 +6 +6 3x+10=13x-3x -3x 10=10x x=1 10 10
  64. 64. Solve: 15x+4=8x+32
  65. 65. Solve: 15x+4=8x+321. Rearrange equation 7x=28
  66. 66. Solve: 15x+4=8x+321. Rearrange equation 7x=282. Divide by 7 x=4
  67. 67. Solve: 15x+4=8x+321. Rearrange equation 7x=282. Divide by 7 x=43. Check Solution 15(4)+4=8(4)+32 60 +4= 32 +32
  68. 68. Solve: 15x+4=8x+321. Rearrange equation 7x=282. Divide by 7 x=43. Check Solution 15(4)+4=8(4)+32 60 +4= 32 +32 64 = 64
  69. 69. Solve: 15x+4=8x+321. Rearrange equation 7x=282. Divide by 7 x=43. Check Solution 15(4)+4=8(4)+32 60 +4= 32 +32 64 = 64 
  70. 70. Work for the problem 15x+4=8x+32
  71. 71. Work for the problem 15x+4=8x+32 15x+4=8x+32 -4 -4 15x = 8x+28
  72. 72. Work for the problem 15x+4=8x+32 15x+4=8x+32 -4 -4 15x = 8x+28 -8x -8x _ 7x = 28
  73. 73. Work for the problem 15x+4=8x+32 15x+4=8x+32 -4 -4 15x = 8x+28 -8x -8x _ 7x = 28 7 7
  74. 74. Work for the problem 15x+4=8x+32 15x+4=8x+32 -4 -4 15x = 8x+28 -8x -8x _ 7x = 28 7 7 x = 4
  75. 75. Special Cases
  76. 76. Special CasesThere are 2 ‘special cases’ in solving these types of equations.
  77. 77. Special CasesThere are 2 ‘special cases’ in solving these types of equations.The first will leave you with NO SOLUTION where the second will leave you with an infinite amount of solutions.
  78. 78. Special CasesThere are 2 ‘special cases’ in solving these types of equations.The first will leave you with NO SOLUTION where the second will leave you with an infinite amount of solutions.If there is NO SOLUTION this means no matter what you plug in for the variable the equation will never work
  79. 79. Special CasesThere are 2 ‘special cases’ in solving these types of equations.The first will leave you with NO SOLUTION where the second will leave you with an infinite amount of solutions.If there is NO SOLUTION this means no matter what you plug in for the variable the equation will never workIf there is an infinite amount of solutions it means that ANY number you plug in for the variable will cause the equation to be equal and correct.
  80. 80. Special Case #1
  81. 81. Special Case #1 NO SOLUTION
  82. 82. Special Case #1 NO SOLUTION 4x-2=4x+6 -4x -4x _ -2 = 6
  83. 83. Special Case #1 NO SOLUTION 4x-2=4x+6 -4x -4x _ -2 = 6This can NEVER be true.
  84. 84. Special Case #1 NO SOLUTION 4x-2=4x+6 -4x -4x _ -2 = 6This can NEVER be true.Answer: NO SOLUTION
  85. 85. Special Case #2
  86. 86. Special Case #2Infinite number of solutions
  87. 87. Special Case #2Infinite number of solutions 7x+4=2x+5x+4 7x+4=7x+4 -7x -7x _ 4= 4
  88. 88. Special Case #2Infinite number of solutions 7x+4=2x+5x+4 7x+4=7x+4 -7x -7x _ 4= 4This is ALWAYS true. So ‘x’ can equal ANY number
  89. 89. Special Case #2
  90. 90. Special Case #2Additional method of solving
  91. 91. Special Case #2Additional method of solving 7x+4=2x+5x+4 7x+4=7x+4 -4 -4_ 7x = 7x 7 7 x=x
  92. 92. Special Case #2 Additional method of solving 7x+4=2x+5x+4 7x+4=7x+4 -4 -4_ 7x = 7x 7 7 x=xShows that ANY number can be the solution
  93. 93. What if the problem is set up differently?
  94. 94. What if the problem is set up differently?Problems may be set up with additional steps that must be taken prior to being able to solve the equation. The main focus will be to know how to manipulate the equation so it is set up in the way we just learned how to solve it.
  95. 95. What if the problem is set up differently?Problems may be set up with additional steps that must be taken prior to being able to solve the equation. The main focus will be to know how to manipulate the equation so it is set up in the way we just learned how to solve it.Never fear a problem. SOLVE it!
  96. 96. 3(2x-4)=4x+8
  97. 97. 3(2x-4)=4x+8Let’s Solve:3(2x-4)=4x+8 Distribute the 3 to the 2x & -4
  98. 98. 3(2x-4)=4x+8Let’s Solve:3(2x-4)=4x+8 Distribute the 3 to the 2x & -4 6x-12 =4x+8 Now the equation is ready to be solved.
  99. 99. 3(2x-4)=4x+8Let’s Solve:3(2x-4)=4x+8 Distribute the 3 to the 2x & -4 6x-12 =4x+8 Now the equation is ready to be solved.-4x -4x _ 2x-12= 8
  100. 100. 3(2x-4)=4x+8Let’s Solve:3(2x-4)=4x+8 Distribute the 3 to the 2x & -4 6x-12 =4x+8 Now the equation is ready to be solved.-4x -4x _ 2x-12= 8 +12 +12 2x = 20
  101. 101. 3(2x-4)=4x+8Let’s Solve:3(2x-4)=4x+8 Distribute the 3 to the 2x & -4 6x-12 =4x+8 Now the equation is ready to be solved.-4x -4x _ 2x-12= 8 +12 +12 2x = 20 2 2
  102. 102. 3(2x-4)=4x+8Let’s Solve:3(2x-4)=4x+8 Distribute the 3 to the 2x & -4 6x-12 =4x+8 Now the equation is ready to be solved.-4x -4x _ 2x-12= 8 +12 +12 x=10 2x = 20 2 2
  103. 103. Now you know…..

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