Solve `|x-3|+|x-2|=1.`

Explanation

To solve the equation \( |x-3| + |x-2| = 1 \), we will consider the critical points where the expressions inside the absolute values change sign. These points are \( x = 2 \) and \( x = 3 \). We will analyze the equation in three cases based on these points.

### Step 1: Identify the cases based on critical points
The critical points divide the number line into three intervals:
1. \( x < 2 \)
2. \( 2 \leq x < 3 \)
3. \( x \geq 3 \)

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