Solving Equations with Algebra Tiles: The basics

Each small square is a unit tile. For the equations we will solve, we will use 2 types of algebra tiles. A single red, or shaded, unit tile represents the number -1. A single yellow, or unshaded, unit tile represents the number 1. Each rectangle is an x-bar, or a variable bar. A single green, or unshaded, x-bar represents 1x. A single red, or shaded, x-bar represents -1x.

Two main ideas that you need for solving equations The goal of solving equations: To get one x alone on one side of the equation. The rule for solving equations: Do the same thing to both sides of the equation.

Let’s model the basic equation… x + 2 = 7 x + 2 = 7 Remember, our goal is to get one x alone, and we must do the exact same thing to both sides of the equation. To get the x bar alone, take 2 units from each side. The x bar that remains balances with 5 units. X = 5

Let’s try another basic equation… 3x = 15 3x = 15 To get x alone, we must do the exact same thing to both sides of the equation. We cannot take anything away, since we couldn’t take the same things from both sides. To get each x bar alone, split both sides into 3 groups. X = 5 In each group, 1 x-bar balances with 5 units.

Now let’s try… 2x + 1 = 7 2x + 1 = 7 Take 1 unit from each side to get the x term alone. Split both sides into 2 groups to get each x alone. In each group, 1 x bar balances with three units. X = 3

One more…. 11 = 4x = 4x + 7 Take 7 units from each side to get the x term alone. Split both sides into 4 groups to get each x alone. In each group, 1 x bar balances with 1 unit. 1 = x