We are given a linear equation and asked to solve for $x$. The equation is: $-4 - 3(5x - 6) = -4(-x - 1) + 6$

1. Problem Description

We are given a linear equation and asked to solve for $x$. The equation is:

$-4 - 3(5x - 6) = -4(-x - 1) + 6$

2. Solution Steps

First, we distribute the $-3$ on the left side of the equation and the $-4$ on the right side:

$-4 - 3(5x - 6) = -4(-x - 1) + 6$

$-4 - 15x + 18 = 4x + 4 + 6$

Next, we combine like terms on both sides of the equation:

$-15x + 14 = 4x + 10$

Now, we isolate the $x$ terms by adding $15x$ to both sides:

$-15x + 14 + 15x = 4x + 10 + 15x$

$14 = 19x + 10$

Subtract 10 from both sides:

$14 - 10 = 19x + 10 - 10$

$4 = 19x$

Finally, we divide both sides by $19$ to solve for $x$:

$\frac{4}{19} = \frac{19x}{19}$

$x = \frac{4}{19}$

3. Final Answer

$x = \frac{4}{19}$