There are many different models that you could use to set up and solve one-variable equations. In this section, you will use algebra tiles to set up and solve one-variable equations involving the operations of addition and subtraction.

For algebra tiles, a rectangle represents the variable, usually x, and squares are used to represent numbers.

Consider the equation x − 1 = 2. This equation can be modeled with algebra tiles using one green rectangle (positive x-tile) and 1 red square (negative unit tiles) on the left side of an equal sign and 2 yellow squares (positive unit tiles) on the right side of an equal sign.

Watch this equation being solved using the algebra tile model in a video.

Use the interactive linked to the image below to set up and solve equations with algebra tiles on your own.

• Click the “New Equation” button, the piece of paper in the yellow panel, to generate a one-step equation of the form x + b = c or x − b = c.
• Use the tools to set up the equation and click the Check tool to check your model.
• Once you have the correct setup, use zero pairs and remove tiles as necessary to solve the equation.
• Type your solution into the text box, and click the Check tool to check your answer.

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Pause and Reflect

How does the algebra tile model allow you to better visualize the concept of zero pairs?

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Check Your Answer

Zero pairs are a combination of one positive and one negative tile that add to 0. The algebra tile model shows a yellow/green positive tile next to a red negative tile.

How are addition and subtraction related, and what does that tell you about how to solve equations involving addition or subtraction?

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Check Your Answer

Addition and subtraction are inverse operations. When you solve an equation, you use inverse operations to “undo” the operation that is being done to the variable. To solve the equation, you add the opposite of the addend or minuend in order to get the variable by itself.

Practice

For Questions 1 – 3, use the algebra tile model to determine the value of x.

1. x − 5 = 15
   
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   How many positive unit tiles need to be added to both sides of the equation in order to make enough zero pairs to move the 5 negative unit tiles on the left side of the equation?
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   Check Your Answer

   x = 20
2. x + 7 = 3
   
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   How many negative unit tiles need to be added to both sides of the equation in order to make enough zero pairs to move the 7 positive unit tiles on the left side of the equation?
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   Check Your Answer

   x = -4
3. x − 5 = 4
   

   Use the griddable response interactive below to record and check your answer.

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   Need a hint?

   How many positive unit tiles need to be added to both sides of the equation in order to make enough zero pairs to move the 5 negative unit tiles on the left side of the equation?