Let's solve the equation step by step:
Start with the original equation: \[ 1 - 2(5 + 3x) = 15 \]
Distribute \(-2\) through the parentheses: \[ 1 - 10 - 6x = 15 \]
Combine like terms (1 - 10): \[ -9 - 6x = 15 \]
Add 9 to both sides of the equation: \[ -6x = 15 + 9 \] \[ -6x = 24 \]
Divide both sides by -6: \[ x = \frac{24}{-6} \] \[ x = -4 \]
So, the solution to the equation \(1 - 2(5 + 3x) = 15\) is: \[ \boxed{-4} \]
