We can start by graphing the two sides of the equation separately.
For $|x-1|$, this is a V-shaped graph with the vertex at (1,0).
For $|x-2| + |x-3|$, this is a W-shaped graph with vertices at (2,0) and (3,0).
The equation $|x-1| = |x-2| + |x-3|$ represents the points where the two graphs intersect.
From the graph, we can see that there are $\boxed{2}$ points of intersection, so there are 2 real solutions for x.
The answer is: 2
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the number of real solutions for x in the equation $|x-1| = |x-2| + |x-3|$?

### Answer:
