Let's start with the equation:
\[ \frac{2}{3}(7 + 3m) = 3 + 3m \]
To eliminate the fraction, we multiply both sides of the equation by 2. Here are the steps:
- Multiply both sides by 2:
\[ 2 \cdot \frac{2}{3}(7 + 3m) = 2 \cdot (3 + 3m) \]
- Simplifying the left side:
\[ \frac{2 \cdot 2}{3}(7 + 3m) = \frac{4}{3}(7 + 3m) \]
- Simplifying the right side:
\[ 2(3 + 3m) = 6 + 6m \]
Now, we have the new equation:
\[ \frac{4}{3}(7 + 3m) = 6 + 6m \]
To find what \((7 + 3m)\) equals in terms of fractions, we can express it as:
\[ (7 + 3m) = \frac{?}{\frac{4}{3}} \]
To solve for \(7 + 3m\), we rearrange this:
\[ 7 + 3m = \frac{3(6 + 6m)}{4} \]
Multiplying both sides by \(\frac{3}{4}\) will ultimately lead us to express \((7 + 3m)\) in a clear form.
Thus, the main focus of your equation simplifies down to \( (7 + 3m) \), and that will be your answer relating to the fraction and whole number equation mentioned above.
However, if your goal is just to present what \( (7 + 3m) \) simplifies to given the context, the answer is:
\[ (7 + 3m) = \frac{3(6 + 6m)}{4} \quad \text{if you want an explicit form}. \]
Otherwise, it is just used as part of the equation results above. If you would like to calculate or give a specific value, further information on \( m \) is needed.
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