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To solve the equation \( -1 - 2 [ x - 3 ( x + 1 ) ] = 4 ( x - 5 ) - 1 \), let's start by simplifying both sides step by step. First, distribute the \( -2 \) on the left side: \[ -1 - 2(x - 3(x + 1)) = -1 - 2(x - 3x - 3) = -1 - 2(-2x - 3) = -1 + 4x + 6 = 4x + 5. \] Now simplify the right side: \[ 4(x - 5) - 1 = 4x - 20 - 1 = 4x - 21. \] So the equation simplifies to: \[ 4x + 5 = 4x - 21. \] Subtract \( 4x \) from both sides: \[ 5 = -21. \] This is a contradiction, indicating that there are no solutions to the equation. The left and right sides are never equal.