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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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1 answer

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 \(-2x + 1\)).