To solve for \( x \) in the equation
\[ \frac{3}{7}x - 4 = -1, \]
first, let's isolate the term with \( x \) by adding 4 to both sides:
\[ \frac{3}{7}x = -1 + 4. \]
Simplifying the right side gives:
\[ \frac{3}{7}x = 3. \]
Next, to solve for \( x \), multiply both sides by the reciprocal of \( \frac{3}{7} \), which is \( \frac{7}{3} \):
\[ x = 3 \cdot \frac{7}{3}. \]
This simplifies to:
\[ x = 7. \]
So the solution is
\[ \boxed{7}. \]