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

Question

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.

Answer 1

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.