Solving Equations

The Algebra Tiles tool has two modes. To switch between these modes, use the arrow in the upper right corner of the tool window.

Model/Solve an Equation Mode

In this mode, use tiles to represent two expressions, then set them equal to create an equation.

Solve a Given Equation Mode

This mode provides ready-to-solve equations. The tiles are set up, and the sides are already set equal. Choose from 1-step equations, 2-step equations, and equations with the variable on both sides by using the buttons below the work area.

An equation is solved by isolating the variable, that is, by getting one positive x-tile alone on a side of the work area.

There are several operations that are useful for solving equations with Algebra Tiles.

Addition and Subtraction:

Add the same number of tiles to each side.
Remove the same number of tiles from each side.
Add pairs of opposite tiles (neutral pairs) to either side. Neutral pairs add to zero, so adding a neutral pair does not change the value of an expression.
Clear neutral pairs from either side. To clear a neutral pair, drag a negative tile onto a positive tile of the same type, or vice-versa. The tiles vanish.

Division:

To model dividing both sides by a number:

Click the arrow below the tile menu and choose the number of regions you want.
Arrange the tiles on each side so they are equally distributed in the regions.
Finally, on each side, remove tiles from all but one of the regions.

For example, to solve 3x = 6:

Divide the work area into 3 regions.
On the left, place 1 x-tile in each region.
On the right, place 2 unit tiles into each region.
On each side, remove the tiles from all but one region.

The work area shows 1 x-tile on the left and 2 unit tiles on the right The readout shows the solution x = 2.

Checking Your Solution:

When you have isolated the variable, click "Check Solution" to see if your solution is correct.