The problem asks to solve the following equation for $x$: $[5x + (8 + 3x) - 19] - 1 = 1 - [-2x + (7x - 65)]$

1. Problem Description

The problem asks to solve the following equation for $x$:

$[5x + (8 + 3x) - 19] - 1 = 1 - [-2x + (7x - 65)]$

2. Solution Steps

First, we simplify the expressions within the brackets.

$[5x + (8 + 3x) - 19] - 1 = 1 - [-2x + (7x - 65)]$

$[5x + 8 + 3x - 19] - 1 = 1 - [-2x + 7x - 65]$

$[8x - 11] - 1 = 1 - [5x - 65]$

$8x - 11 - 1 = 1 - 5x + 65$

$8x - 12 = 66 - 5x$

Now, we move the terms with $x$ to the left side and the constant terms to the right side.

$8x + 5x = 66 + 12$

$13x = 78$

Now, we divide both sides by 13 to solve for $x$.

$x = \frac{78}{13}$

$x = 6$

3. Final Answer

$x = 6$