"Motivate" = get someone to do something by whatever means. "Would a 50% pay cut to motivate you to finish your work assignment on time?" “encourage” = make someone brave enough to do something. "She encouraged the orphan to learn and to read." "Inspire" = give spiritual guidance/advice and, eventually, get someone, by gentle means, to do something of positive and/or spiritual nature. "Your painting inspired me to try painting myself."

The answer is too complex to answer here and you really need to refer to a dictionary. The problem is they *can* be interchangeable in some instances, but more often they can't.