Use the image to answer the question.

Question

An illustration shows a rectangular tile equals x, a square tile equals positive 1, and another square equals negative 1.

Which of the following models represents an algebraic expression equivalent to 2(x−1)+3
?

(1 point)
Responses

An illustration shows 2 stacked rectangular tiles and 1 square tile.
Image with alt text: An illustration shows 2 stacked rectangular tiles and 1 square tile.

An illustration shows 2 stacked rectangular tiles and 2 stacked square tiles.
Image with alt text: An illustration shows 2 stacked rectangular tiles and 2 stacked square tiles.

An illustration shows 2 stacked rectangular tiles and 2 stacked square tiles.
Image with alt text: An illustration shows 2 stacked rectangular tiles and 2 stacked square tiles.

An illustration shows 2 stacked rectangular tiles and 1 square tile.

Answer 1

To solve the expression \(2(x - 1) + 3\), we can first simplify it.

1. Begin by distributing the 2: \[ 2(x - 1) = 2x - 2 \]

2. Now, add 3 to this result: \[ 2x - 2 + 3 = 2x + 1 \]

Now, we have the algebraic expression \(2x + 1\).

In terms of the tiles:

• The rectangular tile represents \(x\).
• The square tile representing positive \(1\).

Thus, the expression \(2x + 1\) can be represented as:

• 2 rectangular tiles (for \(2x\))
• 1 square tile (for \(+1\))

From the given options, you need to find the model that includes 2 stacked rectangular tiles and 1 square tile.

Therefore, the correct response is: An illustration shows 2 stacked rectangular tiles and 1 square tile.