Answer: It sounds as though the gas powered weed whacker was a bit too powerful for your needs. If the line is breaking, it's because you're getting too close to the growth you want to cut back. You should just touch the weeds and grasses you want to cut down with the very tip of the line and slowly work your way forward. If you try to take too big a bite, the line will snag and break. It will also break if you continually hit something hard - like a fence post or tree trunk.
If you have a small yard and have access to electricity through outside outlets, I think an electric weed eater will do the job. There are also models that allow you to charge a battery prior to use so you can work without hauling extension cords all around.
As for technique, practice makes perfect. Target only herbacious growth, work slowly from the edge to the center if you're doing a large clump, and stay a safe distance from woody perennials and tree trunks.
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