We start by solving the equation:

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

Step 1: Isolate the absolute value expression

Subtract 3 from both sides:

$|2x - 2| = 5 - 3$

$|2x - 2| = 2$

Step 2: Solve the absolute value equation

Now, we solve the absolute value equation by considering two cases:

Case 1: $2x - 2 = 2$

$2x = 2 + 2$ $2x = 4$ $x = 2$

Case 2: $2x - 2 = -2$

$2x = -2 + 2$ $2x = 0$ $x = 0$

Final solution:

The solutions are:

$x = 2 \quad \text{or} \quad x = 0$

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve equations with multiple absolute value terms?
2. What are the steps to graph the equation $|2x - 2| + 3 = 5$?
3. Can absolute value equations have no solution?
4. What is the difference between solving $|ax + b| = c$ and $ax + b = c$?
5. How do absolute value functions behave when reflected on the x-axis?

Tip: When solving absolute value equations, always remember to consider both the positive and negative cases.