To solve the equation \(-4(2x + 5) + x + 2 = -11\), let's start by distributing the \(-4\) on the left side:
\[ -4 \cdot 2x - 4 \cdot 5 + x + 2 = -11 \]
This simplifies to:
\[ -8x - 20 + x + 2 = -11 \]
Now, combine like terms. Combine the \(x\) terms and the constant terms:
\[ (-8x + x) + (-20 + 2) = -11 \]
This gives us:
\[ -7x - 18 = -11 \]
Next, isolate the term with \(x\) by adding \(18\) to both sides:
\[ -7x - 18 + 18 = -11 + 18 \]
This simplifies to:
\[ -7x = 7 \]
Now, divide both sides by \(-7\):
\[ x = \frac{7}{-7} \]
Thus, we find:
\[ x = -1 \]
So, the solution is:
\[ \boxed{-1} \]