Question
Start by multiplying the left side of the equation by 2 to get rid of the fraction on the left side of the equation.
2
3
(7+3m)
=
3+3m
2 ·
2
3
(7+3m)
=
2 · (3+3m)
(7+3m)
=
?
2
3
(7+3m)
=
3+3m
2 ·
2
3
(7+3m)
=
2 · (3+3m)
(7+3m)
=
?
Answers
GPT-4o mini
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:
1. Multiply both sides by 2:
\[
2 \cdot \frac{2}{3}(7 + 3m) = 2 \cdot (3 + 3m)
\]
2. Simplifying the left side:
\[
\frac{2 \cdot 2}{3}(7 + 3m) = \frac{4}{3}(7 + 3m)
\]
3. 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.
\[
\frac{2}{3}(7 + 3m) = 3 + 3m
\]
To eliminate the fraction, we multiply both sides of the equation by 2. Here are the steps:
1. Multiply both sides by 2:
\[
2 \cdot \frac{2}{3}(7 + 3m) = 2 \cdot (3 + 3m)
\]
2. Simplifying the left side:
\[
\frac{2 \cdot 2}{3}(7 + 3m) = \frac{4}{3}(7 + 3m)
\]
3. 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.