Let's solve the equation step by step:

Given equation:

$4(x - 1) - 2(3x + 5) = 3x - 1$

Step 1: Distribute the constants across the parentheses.

$4(x - 1) = 4x - 4$ $-2(3x + 5) = -6x - 10$

Now, substitute these into the equation: $4x - 4 - 6x - 10 = 3x - 1$

Step 2: Combine like terms on the left-hand side.

$(4x - 6x) - 4 - 10 = 3x - 1$ $-2x - 14 = 3x - 1$

Step 3: Move all terms involving $x$ to one side, and constants to the other side.

$-2x - 3x = -1 + 14$ $-5x = 13$

Step 4: Solve for $x$.

$x = \frac{13}{-5}$ $x = -\frac{13}{5}$

Thus, the solution is: $x = -\frac{13}{5}$

Would you like a detailed breakdown of any step?

Here are some related questions:

1. How do you check the solution to this equation?
2. Can this type of equation have more than one solution?
3. What happens if there is no solution in a similar problem?
4. How can you solve similar equations involving fractions?
5. What if there were quadratic terms, how would the process change?

Tip: Always simplify both sides of an equation as much as possible before moving terms across the equals sign!