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Solving Multistep Equations

Solving Multistep Equations. 2x + 4 = 12. Method 1 : Algebra tiles. You should have a basic understanding of Algebra Tiles to use this tutorial. The Legal Moves are the set of moves allowed. Let’s review the Legal Moves. Method 1 : Algebra tiles. Legal Moves 1. Removing Zero Pairs.

jason-velasquez
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Solving Multistep Equations

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  1. Solving Multistep Equations 2x + 4 = 12

  2. Method 1 : Algebra tiles You should have a basic understanding of Algebra Tiles to use this tutorial. The Legal Moves are the set of moves allowed. Let’s review the Legal Moves.

  3. Method 1 : Algebra tiles Legal Moves 1. Removing Zero Pairs

  4. Removing Zero Pairs + + - - Tiles of opposite types in the same quadrants form zero pairs and can be removed

  5. Removing Zero Pairs + + - - Tiles of the same type in adjacent quadrants form zero pairs and can be removed

  6. Method 1 : Algebra tiles Legal Moves 1. Removing Zero Pairs 2. Flipping Tiles

  7. Flipping Tiles + + + + - - - - Tiles can be flipped over ANY dashed line to change their location

  8. Method 1 : Algebra tiles Legal Moves 1. Removing Zero Pairs 2. Flipping Tiles 3. Dividing into groups

  9. Dividing into Groups + + + + - - 3x = -6 - - x = -2 After separating x’s from unit tiles. Divide the unit tiles into the same number of equal sized groups as there are x’s.

  10. Are you ready for an Example? WARNING!!! There are many possible methods for solving an equation with algebra tiles. You may see a different move…try it and see if you get the same answer!!!!

  11. Putting it all Together Let’s Start with a basic equation: 4x – 7 = 9 + + - -

  12. Putting it all Together Flip up tiles in the (-) region: 4x – 7 = 9 + + - -

  13. Putting it all Together Flip unit tiles away from the region with the x-tiles: 4x = 16 + + - -

  14. Putting it all Together Arrange unit tiles into four equal groups since there are 4 x-tiles: x = 4 4x = 16 + + - -

  15. Putting it all Together x = 4 is the correct answer!!! + + - -

  16. CHECK YOUR ANSWER Plug x = 4 into the original equation 4x – 7 = 9 4(4) - 7 = 9 16 – 7 = 9 9 = 9 Since the statement is true then 4 is a solution!!!

  17. Another Example? WARNING!!! You may setup your negative items as red tiles on top OR other colored tiles on bottom. Either setup is acceptable.

  18. Example 2 Let’s Start with an advanced equation: 2(3 – 2x) = 4 + (-2x) – 10 + + - -

  19. Example 22(3 – 2x) = 4 + (-2x) – 10 Flip up: 6 – 4x = 4 - 2x – 10 + + - -

  20. Example 22(3 – 2x) = 4 + (-2x) – 10 Flip up: 6 – 4x = 4 - 2x – 10 + + - -

  21. Example 22(3 – 2x) = 4 + (-2x) – 10 Remove Zero Pairs: 6 – 4x = - 2x – 6 + + - -

  22. Example 22(3 – 2x) = 4 + (-2x) – 10 Remove more Zero Pairs: 6 – 2x = – 6 + + - -

  23. Example 22(3 – 2x) = 4 + (-2x) – 10 Flip red x-tiles to the other side: 6 = 2x – 6 + + - -

  24. Example 22(3 – 2x) = 4 + (-2x) – 10 Flip red x-tiles to the other side: 6 = 2x – 6 + + - -

  25. Example 22(3 – 2x) = 4 + (-2x) – 10 Flip unit tiles away from the x-tiles: 12 = 2x + + - -

  26. Example 22(3 – 2x) = 4 + (-2x) – 10 Flip unit tiles away from the x-tiles: 12 = 2x + + - -

  27. Example 22(3 – 2x) = 4 + (-2x) – 10 Arrange tiles into 2 group since there are 2 x-tiles: 6 = x + + - -

  28. Example 22(3 – 2x) = 4 + (-2x) – 10 x = 6 is the correct answer!!! + + - -

  29. CHECK YOUR ANSWER Plug x = 6 into the original equation 2(3 – 2x) = 4 + (-2x) – 10 2(3 – 2(6)) = 4 + (-2(6)) – 10 2(3 – 12) = 4 + (-12) – 10 2(-9) = - 8 – 10 • 18 = - 18 Since the statement is true then 6 is a solution!!!

  30. Method 2 : Solve using a Table This method is derived from the rules of algebra tiles so the steps are similar.

  31. Using a Table Let’s solve the equation: 5x – 3(x – 2) = -2x - 4

  32. CHECK YOUR ANSWER Plug x = -2.5 into the original equation 5x – 3(x – 2) = -2x - 4 5(-2.5) – 3(-2.5 – 2) = -2(-2.5) – 4 -12.5 – 3(-4.5) = 5 – 4 -12.5 + 13.5 = 1 1 = 1 Since the statement is true then -2.5 is a solution!!!

  33. Give it a try!!! You should be ready to give it a try on your own. Locate the Checkpoint 1 – Worksheetfrom the Geometry Page on School Fusion, Print it, show all work, and turn it in to your teacher. Once the worksheet is 100% correct then you will be eligible to retake the Checkpoint 1 – Quiz!!!

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