To solve this equation, we need to isolate the variable x.

First, we will combine like terms on both sides of the equation:

22x - 3 = 3x - 22

Next, we will move the variable terms to one side of the equation and the constant terms to the other side. To do this, we will subtract 3x from both sides and add 22 to both sides:

22x - 3x = -22 +3
19x = -19

Finally, we will solve for x by dividing both sides by 19:

x = -19/19
x = -1

Therefore, the solution to the equation 22x - 3 = 3x - 22 is x = -1.