The given equation is:

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

Let's solve it step-by-step:

1. Simplify the right side of the equation by removing the parentheses:

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

So the equation becomes:

$2x - 2 = 2$

2. Add 2 to both sides:

$2x - 2 + 2 = 2 + 2$

$2x = 4$

3. Divide both sides by 2:

$x = \frac{4}{2} = 2$

Solution

The solution to the equation is:

$\boxed{x = 2}$

Would you like more details on any step? Or do you have any other questions? Here are some related questions you might consider:

1. How do you handle equations with multiple variables?
2. What are some common mistakes when solving equations like this?
3. How do parentheses affect equations in algebra?
4. What are other methods for solving linear equations?
5. How can this equation be visualized on a graph?

Tip: Always simplify both sides of an equation as much as possible before solving for the variable.