The equation is:

\[
mw + mv = x
\]

To solve for \( m \), let's factor \( m \) out from the terms on the left-hand side:

\[
m(w + v) = x
\]

Now, divide both sides of the equation by \( (w + v) \) to isolate \( m \):

\[
m = \frac{x}{w + v}
\]

So the solution is:

\[
m = \frac{x}{w + v}
\]

Would you like more details on how this was solved, or do you have any questions?

Here are five related questions to think about:
1. What if \( w + v = 0 \)? What would happen to the equation for \( m \)?
2. How would you solve for \( w \) if \( m \) was known instead?
3. How would you solve for \( x \) if you knew \( m \), \( w \), and \( v \)?
4. What are the potential values of \( m \) when \( w \) and \( v \) are negative?
5. How would this formula change if \( w \) and \( v \) were functions of another variable, say \( t \)?

**Tip**: When factoring out variables, always ensure you're working with a non-zero term to avoid undefined operations like division by zero.

Learn how to solve the equation mw + mv = x for m with a detailed step-by-step solution. This problem involves linear equations and algebraic manipulation, focusing on isolating the variable m. Suitable for students in Grades 7-9.

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