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Which is a correct representation of [tex]\( x - 2 \)[/tex] using algebra tiles?

A. [tex]\[ \begin{array}{c}
x & \square \\
x
\end{array} \][/tex]

B. [tex]\[ \begin{array}{c}
x \\
\square & \square
\end{array} \][/tex]

C. [tex]\[ \begin{array}{c}
\square & \square & \square \\
x
\end{array} \][/tex]

D. [tex]\[ \begin{array}{c}
x - 2
\end{array} \][/tex]

(Note: Adjust the options as necessary based on the intended visual representation of algebra tiles.)



Answer :

GinnyAnswer
To represent [tex]\( x - 2 \)[/tex] using algebra tiles, we need to understand what each type of tile signifies.

- The "x" tile represents the variable [tex]\( x \)[/tex].
- The square ( [tex]\(\square\)[/tex] ) tile represents a positive unit tile, which is [tex]\( +1 \)[/tex].
- To represent a negative unit, we use an empty square with a "-" in front, which is [tex]\( -1 \)[/tex].

So, [tex]\( x - 2 \)[/tex] would be represented by:
- One "x" tile for the [tex]\( x \)[/tex] part.
- Two negative unit tiles ([tex]\( -1 \)[/tex] each) for the [tex]\( -2 \)[/tex] part.

Therefore, the correct representation of [tex]\( x - 2 \)[/tex] using algebra tiles is:
- One "x" tile.
- Two negative unit tiles ([tex]\(-1\)[/tex]).

Putting it all together, [tex]\( x - 2 \)[/tex] can be visualized as:
- [tex]\( x \)[/tex]
- [tex]\( -1 \)[/tex] (empty square)
- [tex]\( -1 \)[/tex] (empty square)

So, the algebra tiles representation for [tex]\( x - 2 \)[/tex] is:
[tex]\[ x \, \text{ } [-1] \, \text{ } [-1] \][/tex]

Or, using simple notation:
- [tex]\( x \, \square \)[/tex]
- [tex]\( x \, [-1] \, [-1] \)[/tex]

The precise configuration is one "x" tile followed by two negative unit tiles.

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