When working with inverse transformations, there are some common mistakes to watch out for:

1. Forgetting the Order: Always do the inverse transformations in the opposite order of how the original ones were done.

   For example, if you first scale a shape by 2 and then move it to the right by 3, you should first move it back to the left by 3 and then scale it down by 0.5.

2. Confusing Inverses: Remember that moving to the right is the opposite of moving to the left.

3. Ignoring Effects: Make sure to consider all the transformations before you use the inverse.

Let’s think about a point, let's call it $P(2, 3)$. This point changes when we apply the transformation $T(x, y) = (2x + 3, y - 1)$. To get back to our original point $P$, we need to do the inverse operations in the right order.

This will help us understand how to reverse the changes correctly!