Model the algebraic expression x + 2. Then select all the statements that are true.

x + 2 cannot be modeled with algebra tiles.
The variable x is represented by a rectangular orange x tile.
The variable x is represented by a square orange + tile.
+ 2 is represented by 2 rectangular orange x tiles.
+ 2 is represented by 2 square orange + tiles.

1 answer

To model the algebraic expression x+2 with algebra tiles:

  1. The variable x is typically represented by a rectangular tile, often colored (in this case, orange).
  2. The constant +2 (the number 2) is represented by two square tiles, also often colored (in this case, orange).

Based on this understanding, let’s evaluate the provided statements:

  1. x+2 cannot be modeled with algebra tiles.

    • False. The expression x+2 can be modeled with algebra tiles.
  2. The variable x is represented by a rectangular orange x tile.

    • True. The variable x is represented by a rectangular tile.
  3. The variable x is represented by a square orange + tile.

    • False. The variable x is not represented by a square tile.
  4. + 2 is represented by 2 rectangular orange x tiles.

    • False. The constant +2 is represented by 2 square tiles, not rectangular tiles.
  5. + 2 is represented by 2 square orange + tiles.

    • True. The constant 2 is represented by 2 square tiles.

Thus, the true statements are:

  • The variable x is represented by a rectangular orange x tile.
  • +2 is represented by 2 square orange + tiles.