Question

Use the image to answer the question.



1 rectangle labeled x, 3 rectangles, each labeled negative x, 3 squares, each labeled 1, and 2 squares, each labeled negative 1
Which model represents an algebraic expression that is equivalent to the algebraic expression represented by the model shown?

(1 point)
Responses

2 rectangles, each labeled negative x, and 1 square labeled 1
Image with alt text: 2 rectangles, each labeled negative x, and 1 square labeled 1

1 rectangle labeled x, 1 rectangle labeled negative x, 2 squares, each labeled 1, and 2 squares, each labeled negative 1
Image with alt text: 1 rectangle labeled x, 1 rectangle labeled negative x, 2 squares, each labeled 1, and 2 squares, each labeled negative 1

3 rectangles, each labeled negative x, and 2 squares, each labeled negative 1
Image with alt text: 3 rectangles, each labeled negative x, and 2 squares, each labeled negative 1

1 rectangle labeled x and 3 squares, each labeled 1
Image with alt text: 1 rectangle labeled x and 3 squares, each labeled 1
Remaining Attempts : 3
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page 17 of 18

Answer 1

To determine which model represents an algebraic expression equivalent to the original model, let's analyze the components given in the first model:

- **1 Rectangle labeled x**: This represents +x.
- **3 Rectangles labeled negative x**: This represents -3x.
- **3 Squares labeled 1**: This represents +3.
- **2 Squares labeled negative 1**: This represents -2.

Now, we can combine these components into an algebraic expression:

\[ x - 3x + 3 - 2 \]

This simplifies to:

\[ -2x + 1 \]

Now we need to evaluate the choices based on what they represent to see which one simplifies to \(-2x + 1\).

1. **2 rectangles, each labeled negative x, and 1 square labeled 1**
- This represents:
\[ -2x + 1 \]
(This matches.)

2. **1 rectangle labeled x, 1 rectangle labeled negative x, 2 squares, each labeled 1, and 2 squares, each labeled negative 1**
- This represents:
\[ x - x + 2 - 2 = 0 \]
(This does not match.)

3. **3 rectangles, each labeled negative x, and 2 squares, each labeled negative 1**
- This represents:
\[ -3x - 2 \]
(This does not match.)

4. **1 rectangle labeled x and 3 squares, each labeled 1**
- This represents:
\[ x + 3 \]
(This does not match.)

The correct response, which is equivalent to the original expression, is:

**2 rectangles, each labeled negative x, and 1 square labeled 1** (equivalent to \(-2x + 1\)).