Negative 3 is less than or equal to x minus 3 less than 2

To solve an extended inequality:  what you do to one part, you must do to all three parts.

You want to get the 'x' all by itself in the center part.

-3  ≤  x - 3 < 2

Add 3:

-3 + 3  ≤  x - 3 + 3 < 2 + 3

       0  ≤  x  < 5