# MODELING EQUATIONS WITH VARIABLES ON BOTH SIDES

## About "Modeling equations with variables on both sides"

Modeling equations with variables on both sides :

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

## Modeling equations with variables on both sides - 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.

Hence, 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.

Hence, 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.

After having gone through the stuff given above, we hope that the students would have understood, how to model equations with variables on both sides

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