MODELING EQUATIONS WITH VARIABLES ON BOTH SIDES

Algebra tiles given below can be used to model equations with variables on both sides.

Solved Examples

Example  1 :

Use algebra tiles to model and solve 2x - 1  =  x + 4.

Solution : 

Step 1 :

Model 2x - 1 on the left side of the mat and x + 4 on the right side. Remember that 2x - 1 is the same as 2x + (-1). 

Step 2 :

Remove one x-tile from both sides. This represents subtracting x from both sides of the equation.

Step 3 :

To isolate 'x' tile on the left side, place one +1-tile on both sides. This represents adding 1 to sides of the equation. 

Step 4 :

Remove zero tiles. 

In the above picture, on the left side, we just have one x-tile and on the right side, we have five +1-tiles. So, one x-tile is equivalent to five +1-tiles. 

So, the solution is x  =  5. 

Example  2 :

Use algebra tiles to model and solve 3x - 1  =  x + 5.

Solution : 

Step 1 :

Model 3x - 1 on the left side of the mat and x + 5 on the right side. Remember that 3x - 1 is the same as 3x + (-1). 

Step 2 :

Remove one x-tile from both sides. This represents subtracting x from both sides of the equation.

Step 3 :

Place one +1-tile on both sides. This represents adding 1 to sides of the equation. 

Step 4 :

Remove zero tiles. 

Step 5 :

Separate each side into 2 equal groups.

One x-tile is equivalent to three +1 tiles. 

So, the solution is x  =  3. 

Reflect

How can we check the solution to the equation 3x -1 = x + 5 using algebra tiles ?

In the original model, replace each x-tile with three +1-tiles. Remove any zero pairs and see if the equation balances.

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