Let's solve the equation step by step:
The given equation is:
\[ -11 + x = -7x - 8(-x + 1) \]
First, simplify the right side:
\[ -8(-x + 1) = 8x - 8 \]
Now, substitute back into the equation:
\[ -11 + x = -7x + 8x - 8 \]
Combine like terms on the right side:
\[ -11 + x = x - 8 \]
Next, subtract \(x\) from both sides:
\[ -11 = -8 \]
This is a false statement, which means the original equation has no solutions.
Summary:
The equation \( -11 + x = -7x - 8(-x + 1) \) has no solutions because it leads to a contradiction.