Literally, "to edge your way around," means to carefully make your way along or around some hazard, like the narrow ledge under the windows of older hotel buildings. It can also be used figuratively, for example: He came to New York determined to make it big in the fashion industry. Only problem, he had no experience in fashion and just a regular high school diploma - and he was impatient and unwilling to work his way up from the bottom.
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