Question

Use the image to answer the question.



3 rectangles, each labeled x, 2 rectangles, each labeled negative x, 5 squares, each labeled 1, and 2 squares, each labeled negative 1
























Which models represent algebraic expressions equivalent to the algebraic expression represented by the model shown?

Select the two correct answers. 

(1 point)
Responses

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

2 rectangles, each labeled x, 1 rectangle labeled negative x, 4 squares, each labeled 1, and 1 square labeled negative 1
Image with alt text: 2 rectangles, each labeled x, 1 rectangle labeled negative x, 4 squares, each labeled 1, and 1 square labeled negative 1

3 rectangles, each labeled x, 1 rectangle labeled negative x, 5 squares, each labeled 1, and 1 square labeled negative 1
Image with alt text: 3 rectangles, each labeled x, 1 rectangle labeled negative x, 5 squares, each labeled 1, and 1 square labeled negative 1

1 rectangle labeled x and 1 square labeled 1
Image with alt text: 1 rectangle labeled x and 1 square labeled 1

1 rectangle, each labeled x and 3 squares, each labeled 1
Image with alt text: 1 rectangle, each labeled x and 3 squares, each labeled 1
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Answer 1

To evaluate which models represent algebraic expressions equivalent to the original model, let's analyze the components of the first model you described:

- **3 rectangles labeled x**
- **2 rectangles labeled -x**
- **5 squares labeled 1**
- **2 squares labeled -1**

Now, let's translate these into an algebraic expression:

1. The total contribution from the rectangles:
- \(3x\) for the \(3\) rectangles labeled \(x\)
- \(2(-x)\) or \(-2x\) for the \(2\) rectangles labeled \(-x\)

Combining these gives:
\[
3x - 2x = x
\]

2. The total contribution from the squares:
- \(5(1)\) or \(5\) for the \(5\) squares labeled \(1\)
- \(2(-1)\) or \(-2\) for the \(2\) squares labeled \(-1\)

Combining these gives:
\[
5 - 2 = 3
\]

Thus, the overall expression represented by the model is:
\[
x + 3
\]

Now we need to find equivalent expressions among the provided options:

1. **Option:** \(2 rectangles, each labeled x, 2 rectangles, each labeled -x, 2 squares, each labeled 1, and 2 squares, each labeled -1\)
- This translates to:
- \(2x - 2x + 2 - 2 = 0\)
- Not equivalent to \(x + 3\).

2. **Option:** \(2 rectangles, each labeled x, 1 rectangle labeled -x, 4 squares, each labeled 1, and 1 square labeled -1\)
- This translates to:
- \(2x - x + 4 - 1 = x + 3\)
- This is equivalent to \(x + 3\).

3. **Option:** \(3 rectangles, each labeled x, 1 rectangle labeled -x, 5 squares, each labeled 1, and 1 square labeled -1\)
- This translates to:
- \(3x - x + 5 - 1 = 2x + 4\)
- Not equivalent to \(x + 3\).

4. **Option:** \(1 rectangle labeled x and 1 square labeled 1\)
- This translates to:
- \(x + 1\)
- Not equivalent to \(x + 3\).

5. **Option:** \(1 rectangle labeled x and 3 squares, each labeled 1\)
- This translates to:
- \(x + 3\)
- This is also equivalent to \(x + 3\).

Thus, the two correct answers are:

- **Option 2:** \(2 rectangles, each labeled x, 1 rectangle labeled -x, 4 squares, each labeled 1, and 1 square labeled -1\)
- **Option 5:** \(1 rectangle labeled x and 3 squares, each labeled 1\)