Investigation: Modeling equations

We can use algebra tiles to model and solve equations with integers. Let's look at some examples, and then try a few of our own.

Using addition to solve an equation

 

Use algebra tiles to model and solve the following equations. Virtual algebra tiles are available at this link.

1. x + 4 = - 2
2. x - 3 = - 2
3. - 6 = x - 3
4. 4 = 7 - x

Reflection

5. Explain why, in the example shown above, it is important to add two +1-tiles to each side and not just the left side of the equation.
6. The example uses a property called the addition property of equality. Explain in your own words what this property allows you to do.

Using division to solve an equation

Worked example

Practice questions

Use algebra tiles to model and solve the following equations. Virtual algebra tiles are available at this link.

7. 2 x = 4
8. 5 x = 15
9. 3 x = - 18
10. 4 x = - 12

Reflection

11. The example uses a property called the division property of equality. Explain in your own words what this property allows you to do.

Extension

12. There are two more properties of equality - the subtraction property of equality and the multiplication property of equality. See if you can demonstrate them using algebra tiles.
13. Explain how you could use algebra tiles to solve an equation like  3 x - 2 = 4.