To use the distributive property to multiply each side of the equation by 2, we start with the equation:
\[ \frac{2}{3}(7 + 3m) = 3 + 3m \]
Now we multiply both sides of the equation by 2:
\[ 2 \cdot \frac{2}{3}(7 + 3m) = 2 \cdot (3 + 3m) \]
Now, let's simplify both sides:
Left Side: \[ 2 \cdot \frac{2}{3}(7 + 3m) = \frac{4}{3}(7 + 3m) \] Applying the distributive property: \[ \frac{4}{3} \cdot 7 + \frac{4}{3} \cdot 3m = \frac{28}{3} + \frac{12m}{3} = \frac{28}{3} + 4m \]
Right Side: \[ 2 \cdot (3 + 3m) = 2 \cdot 3 + 2 \cdot 3m = 6 + 6m \]
Now, we can write the resulting equation:
\[ \frac{28}{3} + 4m = 6 + 6m \]
So the final equation after applying the distributive property is:
\[ \frac{28}{3} + 4m = 6 + 6m \]