Let's revisit the equation to clarify how we arrived at \(-4x\).

### Original Equation:
\[
3x - 5y = 7x + 2y
\]

### Step 1: Move all terms involving \(x\) to one side of the equation.
We subtract \(7x\) from both sides:
\[
3x - 7x - 5y = 2y
\]

### Step 2: Move all terms involving \(y\) to the other side.
We add \(5y\) to both sides:
\[
-4x = 7y
\]

### Conclusion:
When we subtracted \(7x\) from \(3x\), we got \(-4x\), which is why the coefficient of \(x\) is \(-4\).

So, the equation simplifies to:
\[
-4x = 7y
\]
And when solved for \(y\):
\[
y = \frac{-4x}{7}
\]

Does this explanation clear things up? 

Here are 5 related questions:
1. What happens if you multiply both sides of \(-4x = 7y\) by \(-1\)?
2. How would you solve \(4x + 5y = 7x - 2y\)?
3. What if you add \(7x\) to both sides instead of subtracting it?
4. Can you find \(x\) in terms of \(y\) instead of \(y\) in terms of \(x\)?
5. What would the solution look like if we had \(3x + 5y = 7x - 2y\)?

**Tip:** Always carefully perform operations like addition or subtraction on both sides of an equation to avoid sign errors.

Explore how to understand and solve the equation -4x = 7y step-by-step. This explanation covers algebraic concepts involving equations and variables. Suitable for students in Grades 7-9.

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