Distributing and combining like terms, we have \[
\begin{aligned} -3(x^4 - x^3 + x) + 7(x^4 + 2) - 4(2x^4 + 2x^2 + 1) &= -3x^4 + 3x^3 - 3x + 7x^4 + 14 - 8x^4 - 8x^2 - 4 \\ &= (7 - 3 - 8)x^4 + 3x^3 - 3x - 8x^2 + 10 \\ &= -4x^4 + 3x^3 - 8x^2 - 3x + 10. \end{aligned}
\]The leading coefficient of this polynomial is $\boxed{-4}$.
The answer is: -4
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
After simplifying the expression $-3(x^4 - x^3 + x) + 7(x^4 + 2) - 4(2x^4 + 2x^2 + 1)$, what is the leading coefficient of the resulting polynomial?

### Answer:
