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

Removing Zero Pairs ++ --

++ --

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

Flipping Tiles

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

Dividing into Groups x = -6 x = -2

Are you ready for an Example?

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

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

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

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

Putting it all Together x = 4 is the correct 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?

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

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

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

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

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

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

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

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

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

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

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

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 – = - 18 Since the statement is true then 6 is a solution!!!

Method 2 : Solve using a Table

Using a Table Let’s solve the equation: 5x – 3(x – 2) = -2x - 4 EQUATIONREASON 5x – 3(x – 2) = -2x – 4 Original Equation 5x – 3x + 6 = -2x – 4Distributive Property 2x + 6 = -2x – 4Combined like terms 4x + 6 = -4(Flipped -2x) Added 2x to both sides 4x = -10(flipped 6) Subtracted 6 from both sides x = - 2.5Divided both sides by 4

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) – – 3(-4.5) = 5 – = 1 1 = 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!!!