Juanita wants to model the equation 3 x + 2 = negative x + 6. She begins with the tiles below.

Question

3 x tiles and 2 positive 1 tiles = 1 negative x tile

How can Juanita complete her model?
Put 4 yellow unit tiles on the left side of the equal sign.
Put 4 yellow unit tiles on the right side of the equal sign.
Put 6 green x-tiles on the right side of the equal sign.
Put 6 yellow unit tiles on the right side of the equal sign.

Answer 1

To complete Juanita's model for the equation \(3x + 2 = -x + 6\), we can follow the steps to balance both sides of the equation.

1. Understanding the equation: We have \(3x + 2\) on the left side and \(-x + 6\) on the right side.

2. Visualizing the current model:

   • The left side currently has \(3\) x-tiles and \(2\) yellow unit tiles.
   • The right side has \(1\) negative x-tile (which can be represented as \(-x\)).

3. Balancing x-tiles:

   • There are \(3x\) tiles on the left and \(-x\) on the right, which means we need to get \(4\) x-tiles on the right side to balance the equation (since \(3x\) from the left side and \(-x\) from the right equals \(4x\)).
   • To achieve this, we can put \(6 x\) tiles on the right side and \(4 x\) tiles on the left side (which means we need \(3x + 1x = 4x\) on the left).

4. Balancing the constant units:

   • The left side has \(2\) units and the right needs to total \(6\). To balance it to \(6\), we already have \(6\) representing the positive units on the right side.

Putting this all together, we can add the corresponding tiles to complete the model:

• What to do:
  • Put \(4\) yellow unit tiles on the left side of the equal sign.
  • Put \(6\) green x-tiles on the right side of the equal sign (to balance the x's).
  • Keep \(6\) yellow unit tiles on the right side (to match).

Thus, the overall structure balances both sides correctly.