Solving multistep equations
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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.

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Method 1 algebra tiles
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 tiles1
Method 1 : Algebra tiles

Legal Moves

1. Removing Zero Pairs


Removing zero pairs
Removing Zero Pairs

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Tiles of opposite types in the same quadrants form zero pairs and can be removed


Removing zero pairs1
Removing Zero Pairs

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Tiles of the same type in adjacent quadrants form zero pairs and can be removed


Method 1 algebra tiles2
Method 1 : Algebra tiles

Legal Moves

1. Removing Zero Pairs

2. Flipping Tiles


Flipping tiles
Flipping Tiles

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Tiles can be flipped over ANY dashed line to change their location


Method 1 algebra tiles3
Method 1 : Algebra tiles

Legal Moves

1. Removing Zero Pairs

2. Flipping Tiles

3. Dividing into groups


Dividing into groups
Dividing into Groups

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3x = -6

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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.


Are you ready for an example
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!!!!


Putting it all together
Putting it all Together

Let’s Start with a basic equation:

4x – 7 = 9

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Putting it all together1
Putting it all Together

Flip up tiles in the (-) region:

4x – 7 = 9

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Putting it all together2
Putting it all Together

Flip unit tiles away from the region with the x-tiles:

4x = 16

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Putting it all together3
Putting it all Together

Arrange unit tiles into four equal groups since there are 4 x-tiles: x = 4

4x = 16

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Putting it all together4
Putting it all Together

x = 4

is the correct answer!!!

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Check your answer
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!!!


Another example
Another Example?

WARNING!!!

You may setup your negative items as red tiles on top OR other colored tiles on bottom. Either setup is acceptable.


Example 2
Example 2

Let’s Start with an advanced equation:

2(3 – 2x) = 4 + (-2x) – 10

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Example 2 2 3 2x 4 2x 10
Example 22(3 – 2x) = 4 + (-2x) – 10

Flip up:

6 – 4x = 4 - 2x – 10

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Example 2 2 3 2x 4 2x 101
Example 22(3 – 2x) = 4 + (-2x) – 10

Flip up:

6 – 4x = 4 - 2x – 10

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Example 2 2 3 2x 4 2x 102
Example 22(3 – 2x) = 4 + (-2x) – 10

Remove Zero Pairs:

6 – 4x = - 2x – 6

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Example 2 2 3 2x 4 2x 103
Example 22(3 – 2x) = 4 + (-2x) – 10

Remove more Zero Pairs:

6 – 2x = – 6

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Example 2 2 3 2x 4 2x 104
Example 22(3 – 2x) = 4 + (-2x) – 10

Flip red x-tiles to the other side:

6 = 2x – 6

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Example 2 2 3 2x 4 2x 105
Example 22(3 – 2x) = 4 + (-2x) – 10

Flip red x-tiles to the other side:

6 = 2x – 6

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Example 2 2 3 2x 4 2x 106
Example 22(3 – 2x) = 4 + (-2x) – 10

Flip unit tiles away from the x-tiles:

12 = 2x

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Example 2 2 3 2x 4 2x 107
Example 22(3 – 2x) = 4 + (-2x) – 10

Flip unit tiles away from the x-tiles:

12 = 2x

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Example 2 2 3 2x 4 2x 108
Example 22(3 – 2x) = 4 + (-2x) – 10

Arrange tiles into 2 group since there are 2 x-tiles:

6 = x

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Example 2 2 3 2x 4 2x 109
Example 22(3 – 2x) = 4 + (-2x) – 10

x = 6

is the correct answer!!!

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Check your answer1
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!!!


Method 2 solve using a table
Method 2 : Solve using a Table

This method is derived from the rules of algebra tiles so the steps are similar.


Using a table
Using a Table

Let’s solve the equation: 5x – 3(x – 2) = -2x - 4


Check your answer2
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!!!


Give it a try
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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