To determine which expressions are equal to \( \frac{1}{3}(9m + 18) \), we first need to simplify \( \frac{1}{3}(9m + 18) \).
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Distribute \( \frac{1}{3} \) to both terms inside the parentheses:
\[ \frac{1}{3}(9m + 18) = \frac{1}{3} \cdot 9m + \frac{1}{3} \cdot 18 = 3m + 6 \]
Now we need to find the expressions among the options that are equal to \( 3m + 6 \):
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A. \( 3(m + 2) = 3m + 6 \) (Equal)
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B. \( 3 + 6m \) (Not equal, this simplifies to \( 6m + 3 \))
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C. \( 3(1 + 2m) = 3 + 6m \) (Not equal, same as B)
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D. \( 3m + 18 \) (Not equal)
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E. \( 3m + 6 \) (Equal)
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F. \( 3(m + 6) = 3m + 18 \) (Not equal)
Based on the simplifications, the two expressions that are equal to \( \frac{1}{3}(9m + 18) \) are:
A. \( 3(m + 2) \)
E. \( 3m + 6 \)