To solve the equation \( \frac{3}{7}x - 4 = -1 \), follow these steps:
- Add 4 to both sides of the equation to isolate the term with \( x \):
\[ \frac{3}{7}x - 4 + 4 = -1 + 4 \]
This simplifies to:
\[ \frac{3}{7}x = 3 \]
- To eliminate the fraction, multiply both sides by \( \frac{7}{3} \):
\[ \frac{7}{3} \cdot \frac{3}{7}x = 3 \cdot \frac{7}{3} \]
This simplifies to:
\[ x = 7 \]
So the solution is:
\[ \boxed{7} \]