Question

Which finds the solution to the equation represented by the model below?

2 x tiles = 1 x tile and 3 positive 1 tiles
removing 1 x-tile from each side
removing 3 unit tiles from the right side
adding 3 positive unit tiles to each side
arranging the tiles into equal groups to match the number of x-tiles

Answer 1

To solve the equation represented by the model "2 x tiles = 1 x tile and 3 positive 1 tiles", we can break down the steps outlined:

1. Start with the equation:
\[ 2x = 1x + 3 \]

2. Remove 1 x-tile from each side:
\[ 2x - 1x = 1x - 1x + 3 \]
This simplifies to:
\[ x = 3 \]

3. Next, remove 3 unit tiles from the right side:
Since there's no term on the left to remove from that side, the equation remains the same in this context.

4. Add 3 positive unit tiles to each side:
\[ x + 3 = 3 \]

5. Arrange the tiles into equal groups to match the number of x-tiles:
This means we can rewrite the equation if necessary, though it doesn't change since \( x = 3 \) has already been determined.

At every step, the operations maintain the equality of the equation. Consequently, the solution to the equation \( 2x = 3 + x \) is:

\[
\boxed{3}
\]