Question

Now, use the distributive property to multiply the right side of the equation by 2.
2
3
​
(7+3m)
=
3+3m

2 ·
2
3
​
(7+3m)
=
2 · (3+3m)

3(7+3m)
=

Answer 1

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:

\[
\frac{28}{3} + 4m = 6 + 6m
\]