To solve the question, we need to express \( x \cdot 8 \frac{1}{3} \) as an algebraic expression.
First, we can convert the mixed number \( 8 \frac{1}{3} \) into an improper fraction. The mixed number represents:
\[ 8 \frac{1}{3} = 8 + \frac{1}{3} = \frac{24}{3} + \frac{1}{3} = \frac{25}{3} \]
Now, if we multiply \( x \) by the mixed number, we have:
\[ x \cdot 8 \frac{1}{3} = x \cdot \frac{25}{3} = \frac{25x}{3} \]
However, since the question is asking for an expression that uses the components of the mixed number directly, we'll redistribute this as:
\[ x \cdot 8 \frac{1}{3} = x \cdot (8 + \frac{1}{3}) = x \cdot 8 + x \cdot \frac{1}{3} = 8x + \frac{1}{3}x \]
None of the options directly match \( \frac{25x}{3} \), but we can work with \( \frac{1}{3}x \):
Now let’s analyze the given options:
A) \( 8x + 13x \)
This simplifies to \( 21x \), which is not correct.
B) \( 8x - 13x \)
This simplifies to \( -5x \), which is not correct.
C) \( 8 + 13x \)
This is an expression in terms of \( x \) but does not represent the multiplication of \( x \) with \( 8 \frac{1}{3} \).
D) \( 8 - 13x \)
This also does not represent it correctly.
Based on what I derived, none of the provided answers directly express \( x \cdot 8 \frac{1}{3} \) correctly in the conventional sense. However, if we are strictly to choose from the presented options based on what was shown, the first choice seems most like a sum, though it isn't a direct match for the initial equation.
The answer would still be closest to option A: A) \( 8x + 13x \) although conceptually, we should still note that it does not accurately reflect \( x \cdot 8 \frac{1}{3} \)'s conversion. Be sure to double-check the exact terms in your question as it could have nuances in formatting.
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