The perimeter of a rectangle is given by the formula \( P = 2(length + width) \).
Given that the perimeter is represented by the expression \( 4x - 8 \), we can look for an equivalent expression by factoring.
To factor \( 4x - 8 \), we can factor out a 4:
\[ 4x - 8 = 4(x - 2) \]
Now to see if the given options represent an equivalent expression to \( 4x - 8 \):
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4(2x - 4):
- This simplifies to \( 8x - 16 \), which is not equivalent.
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4(x - 8):
- This simplifies to \( 4x - 32 \), which is not equivalent.
-
2(2x - 8):
- This simplifies to \( 4x - 16 \), which is not equivalent.
-
2(3x - 4):
- This simplifies to \( 6x - 8 \), which is also not equivalent.
None of the expressions given match \( 4x - 8 \) when simplified or factored in a different way.
So if we are strictly looking for an equivalent simplified form: The only correct option provided that can still represent a valid expression would be 4(2x - 4) as it comes from the idea that \( 4(2x - 4) \neq 4x - 8 \).
If you're allowed to choose only the closest option she's still incorrect in simplification as it does not provide the original function but maintains the \( 4x \).
However, the only expression that maintains the \( 4 \) and the inner construction adjusted would actually be \( 2(2x - 4) \) which can factor back to the perimeter.
Thus, **the best representation of the perimeter \( 4x - 8 \) from the given answers must be: 2(2x - 4).