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. - PowerPoint PPT Presentation

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Solving Multistep Equations

Solving Multistep Equations2x + 4 = 12Method 1 : Algebra tilesYou should have a basic understanding of Algebra Tiles to use this tutorial.

The Legal Moves are the set of moves allowed. Lets review the Legal Moves.Method 1 : Algebra tilesLegal Moves1. Removing Zero PairsRemoving Zero Pairs++--Tiles of opposite types in the same quadrants form zero pairs and can be removedRemoving Zero Pairs++--Tiles of the same type in adjacent quadrants form zero pairs and can be removedMethod 1 : Algebra tilesLegal Moves1. Removing Zero Pairs

2. Flipping TilesFlipping Tiles++--Tiles can be flipped over ANY dashed line to change their location++--Method 1 : Algebra tilesLegal Moves1. Removing Zero Pairs

2. Flipping Tiles

3. Dividing into groupsDividing into Groups++--After separating xs from unit tiles. Divide the unit tiles into the same number of equal sized groups as there are xs.++--3x = -6x = -2Are you ready for an Example?WARNING!!!

There are many possible methods for solving an equation with algebra tiles. You may see a different movetry it and see if you get the same answer!!!!Putting it all TogetherLets Start with a basic equation: 4x 7 = 9

++--Putting it all TogetherFlip up tiles in the (-) region: 4x 7 = 9

++--Putting it all TogetherFlip unit tiles away from the region with the x-tiles: 4x = 16

++--Putting it all TogetherArrange unit tiles into four equal groups since there are 4 x-tiles:x = 4 4x = 16

++--Putting it all Togetherx = 4is the correct answer!!!

++--CHECK YOUR ANSWERPlug x = 4 into the original equation4x 7 = 94(4) - 7 = 916 7 = 99 = 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 2Lets Start with an advanced equation: 2(3 2x) = 4 + (-2x) 10

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

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

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

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

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

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

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

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

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

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

++--CHECK YOUR ANSWERPlug x = 6 into the original equation2(3 2x) = 4 + (-2x) 102(3 2(6)) = 4 + (-2(6)) 102(3 12) = 4 + (-12) 102(-9) = - 8 1018 = - 18

Since the statement is true then 6 is a solution!!!

Method 2 : Solve using a TableThis method is derived from the rules of algebra tiles so the steps are similar.Using a TableLets solve the equation: 5x 3(x 2) = -2x - 4

EQUATIONREASON5x 3(x 2) = -2x 4

Original Equation5x 3x + 6 = -2x 4 Distributive Property2x + 6 = -2x 4 Combined like terms4x + 6 = -4(Flipped -2x)Added 2x to both sides4x = -10(flipped 6)Subtracted 6 from both sidesx = - 2.5 Divided both sides by 4CHECK YOUR ANSWERPlug x = -2.5 into the original equation5x 3(x 2) = -2x - 45(-2.5) 3(-2.5 2) = -2(-2.5) 4-12.5 3(-4.5) = 5 4-12.5 + 13.5 = 11 = 1Since 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!!!

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