We are asked to determine the solution set of the equation $2 - 3(1-x) = 4 + (3x - 5)$. The possible answer choices are: one solution $x = 0$, one solution $x = -1$, all real numbers, or no solutions.

1. Problem Description

We are asked to determine the solution set of the equation $2 - 3(1-x) = 4 + (3x - 5)$. The possible answer choices are: one solution $x = 0$, one solution $x = -1$, all real numbers, or no solutions.

2. Solution Steps

First, we simplify the equation:

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

$2 - 3 + 3x = 4 + 3x - 5$

$-1 + 3x = 3x - 1$

Now, we subtract $3x$ from both sides of the equation:

$-1 + 3x - 3x = 3x - 1 - 3x$

$-1 = -1$

Since $-1 = -1$ is always true regardless of the value of $x$, the equation is an identity, and all real numbers are solutions.

3. Final Answer

All real numbers