To solve the equation \( 1 - 2(5 + 3x) = 15 \), follow these steps:
Distribute the \(-2\) into the parentheses: \[ 1 - 10 - 6x = 15 \]
Combine like terms on the left side: \[ -9 - 6x = 15 \]
Add \(9\) to both sides to isolate the term with \(x\): \[ -6x = 15 + 9 \] \[ -6x = 24 \]
Divide both sides by \(-6\) to solve for \(x\): \[ x = \frac{24}{-6} \] \[ x = -4 \]
So the solution to the equation is: \[ \boxed{-4} \]