Use the image to answer the question. Which models represent algebraic expressions equivalent to the algebraic expression represented by the model shown? Select the two correct answers. (1 point) Responses 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 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 Image with alt text: 1 rectangle, each labeled x and 3 squares, each labeled 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 Image with alt text: 1 rectangle labeled x and 1 square labeled 1 Skip to navigation

Answer 1

To determine which models represent algebraic expressions equivalent to the original model, we first need to simplify the given model based on the elements it contains:

1. Original Model:

   • 2 rectangles labeled \(x\)
   • 2 rectangles labeled \(-x\)
   • 2 squares labeled \(1\)
   • 2 squares labeled \(-1\)

   This can be written as: \[ 2x + 2(-x) + 2(1) + 2(-1) \] Simplifying this gives: \[ 2x - 2x + 2 - 2 = 0 \] Thus, the expression equivalent to the original model is \(0\).

Next, we'll analyze each option to see if they also simplify to \(0\).

2. Option 1:

   • 2 rectangles labeled \(x\)
   • 1 rectangle labeled \(-x\)
   • 4 squares labeled \(1\)
   • 1 square labeled \(-1\)

   Simplifies to: \[ 2x - x + 4 - 1 = x + 3 \] (Not equivalent)

3. Option 2:

   • 1 rectangle labeled \(x\)
   • 3 squares labeled \(1\)

   Simplifies to: \[ x + 3 \] (Not equivalent)

4. Option 3:

   • 3 rectangles labeled \(x\)
   • 1 rectangle labeled \(-x\)
   • 5 squares labeled \(1\)
   • 1 square labeled \(-1\)

   Simplifies to: \[ 3x - x + 5 - 1 = 2x + 4 \] (Not equivalent)

5. Option 4:

   • 1 rectangle labeled \(x\)
   • 1 square labeled \(1\)

   Simplifies to: \[ x + 1 \] (Not equivalent)

None of the provided options are equivalent to the original expression \(0\).

If the intent is to find any simplification that leads to this value, only reaffirming or re-checking the options is advised. If there are more models available or if there was an oversight, please provide additional context.