\( 1 - 2 ( 4 - 3 ( x + 1 ) ] = 4 ( x - 5 ) - 1 \)

To solve the equation \( 1 - 2 ( 4 - 3 ( x + 1 ) ) = 4 ( x - 5 ) - 1 \), let’s start with simplifying each side systematically. First, simplify the left side: 1. Distribute -3 across \( (x + 1) \): \( -3x - 3 \) 2. Substitute back: \( 1 - 2(4 - (-3x - 3)) \) 3. Simplifying further gives us \( 1 - 2(4 + 3x + 3) = 1 - 2(3x + 7) \) 4. This becomes \( 1 - 6x - 14 = -6x - 13 \) Now, simplify the right side: 1. Distributing gives us \( 4x - 20 - 1 = 4x - 21 \) Setting both sides equal gives us: \[ -6x - 13 = 4x - 21 \] Let's solve for \( x \): 1. Add \( 6x \) to both sides: \( -13 = 10x - 21 \) 2. Add \( 21 \) to both sides: \( 8 = 10x \) 3. Divide by \( 10 \): \( x = \frac{4}{5} \) So, the final answer is: \[ x = \frac{4}{5} \]