Determine the correct way to model the equation 9x + 2 = 8x + (−6) with algebra tiles.

Question

For the left side of the equation:

positive x-tiles

positive unit tiles

For the right side of the equation

positive x-tiles

negitive unit tile

Answer 1

To model the equation \( 9x + 2 = 8x - 6 \) using algebra tiles, you can represent various components of the equation with specific types of tiles.

Left Side of the Equation: \( 9x + 2 \)

1. Positive x-tiles: You would need 9 positive x-tiles to represent the \( 9x \) term.
2. Positive unit tiles: You would need 2 positive unit tiles to represent the \( +2 \).

Right Side of the Equation: \( 8x - 6 \)

1. Positive x-tiles: You would need 8 positive x-tiles to represent the \( 8x \) term.
2. Negative unit tiles: You would need 6 negative unit tiles to represent the \( -6 \).

Summary

So the setup with algebra tiles would look like this:

• Left side:

  • 9 positive x-tiles
  • 2 positive unit tiles

• Right side:

  • 8 positive x-tiles
  • 6 negative unit tiles

This representation will allow you to visualize the equation and solve it by rearranging the tiles accordingly.