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

+ +

--

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

Removing Zero Pairs

+ +

--

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

+ +

--

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

+ +

--

Method 1 : Algebra tiles

Legal Moves1. Removing Zero Pairs

2. Flipping Tiles

3. Dividing into groups

Dividing into Groups+ +

--

After separating x’s from unit tiles. Divide the unit tiles into the same number of equal sized groups as

there are x’s.

+ +

--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

+ +

--

Putting it all Together

Flip up tiles in the (-) region: 4x – 7 = 9

+ +

--

Putting it all Together

Flip unit tiles away from the region with the x-tiles: 4x = 16

+ +

--

Putting it all Together

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

4x = 16+ +

--

Putting it all Together

x = 4is the correct answer!!!

+ +

--

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

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Flip up: 6 – 4x = 4 - 2x – 10

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Flip up: 6 – 4x = 4 - 2x – 10

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Remove Zero Pairs: 6 – 4x = - 2x – 6

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Remove more Zero Pairs: 6 – 2x = – 6

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Flip red x-tiles to the other side: 6 = 2x – 6

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Flip red x-tiles to the other side: 6 = 2x – 6

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Flip unit tiles away from the x-tiles: 12 = 2x

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Flip unit tiles away from the x-tiles: 12 = 2x

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

Arrange tiles into 2 group since there are 2 x-tiles: 6 = x

+ +

--

Example 22(3 – 2x) = 4 + (-2x) – 10

x = 6is the correct answer!!!

+ +

--

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!!!