solving multistep equations
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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 Moves1. 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 Pairs
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Tiles of the same type in adjacent quadrants form zero pairs and can be removed
Method 1 : Algebra tiles
Legal Moves1. Removing Zero Pairs
2. Flipping Tiles
Flipping Tiles
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Tiles can be flipped over ANY dashed line to change their location
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Method 1 : Algebra tiles
Legal Moves1. Removing Zero Pairs
2. Flipping Tiles
3. Dividing into groups
Dividing into Groups
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After separating x’s from unit tiles. Divide the unit tiles into the same number of equal sized groups as
there are x’s.
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--3x = -6
x = -2
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
Let’s Start with a basic equation: 4x – 7 = 9
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Putting it all Together
Flip up tiles in the (-) region: 4x – 7 = 9
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Putting it all Together
Flip unit tiles away from the region with the x-tiles: 4x = 16
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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 Together
x = 4is the correct answer!!!
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CHECK YOUR ANSWER
Plug x = 4 into the original equation4x – 7 = 9
4(4) - 7 = 916 – 7 = 9
9 = 9Since the statement is true then 4 is a solution!!!
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
Let’s Start with an advanced equation: 2(3 – 2x) = 4 + (-2x) – 10
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Example 22(3 – 2x) = 4 + (-2x) – 10
Flip up: 6 – 4x = 4 - 2x – 10
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Example 22(3 – 2x) = 4 + (-2x) – 10
Flip up: 6 – 4x = 4 - 2x – 10
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Example 22(3 – 2x) = 4 + (-2x) – 10
Remove Zero Pairs: 6 – 4x = - 2x – 6
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Example 22(3 – 2x) = 4 + (-2x) – 10
Remove more Zero Pairs: 6 – 2x = – 6
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Example 22(3 – 2x) = 4 + (-2x) – 10
Flip red x-tiles to the other side: 6 = 2x – 6
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Example 22(3 – 2x) = 4 + (-2x) – 10
Flip red x-tiles to the other side: 6 = 2x – 6
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Example 22(3 – 2x) = 4 + (-2x) – 10
Flip unit tiles away from the x-tiles: 12 = 2x
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Example 22(3 – 2x) = 4 + (-2x) – 10
Flip unit tiles away from the x-tiles: 12 = 2x
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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 22(3 – 2x) = 4 + (-2x) – 10
x = 6is the correct answer!!!
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CHECK YOUR ANSWER
Plug x = 6 into the original equation2(3 – 2x) = 4 + (-2x) – 10
2(3 – 2(6)) = 4 + (-2(6)) – 102(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
This method is derived from the rules of algebra tiles so the steps are similar.
Using a TableLet’s solve the equation: 5x – 3(x – 2) = -2x - 4EQUATION REASON
5x – 3(x – 2) = -2x – 4 Original Equation
5x – 3x + 6 = -2x – 4 Distributive Property
2x + 6 = -2x – 4 Combined like terms
4x + 6 = -4 (Flipped -2x)Added 2x to both sides
4x = -10 (flipped 6)Subtracted 6 from both sides
x = - 2.5 Divided both sides by 4
CHECK YOUR ANSWER
Plug x = -2.5 into the original equation5x – 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 = 11 = 1
Since the statement is true then -2.5 is a solution!!!
Give it a try!!!
You should be ready to give it a try on your own.
Locate the Checkpoint 1 – Worksheet from 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!!!