Question

In which of the following solutions would you multiply both sides of the equation by n?

Solve m - n = p for m.
Solve mn = p for m.
Solve m/n = p for m.
Solve m + n = p for m.

Answer 1

To determine in which solutions you would multiply both sides of the equation by \( n \) to solve for \( m \), let's analyze each equation one by one:

1. **Solve \( m - n = p \) for \( m \)**:
- To isolate \( m \), you would add \( n \) to both sides:
\[
m = p + n
\]
- No multiplication by \( n \) is needed here.

2. **Solve \( mn = p \) for \( m \)**:
- To isolate \( m \), divide both sides by \( n \):
\[
m = \frac{p}{n}
\]
- Again, no multiplication by \( n \) is needed here.

3. **Solve \( \frac{m}{n} = p \) for \( m \)**:
- To isolate \( m \), multiply both sides by \( n \):
\[
m = pn
\]
- Here, you do multiply by \( n \).

4. **Solve \( m + n = p \) for \( m \)**:
- To isolate \( m \), subtract \( n \) from both sides:
\[
m = p - n
\]
- No multiplication by \( n \) is needed here.

In summary, you would multiply both sides of the equation by \( n \) only in the case of **"Solve \( \frac{m}{n} = p \) for \( m \)."**