Unplug the power cord for the water softener.
Twist the knobs on the water-supply valves clockwise to shut off the water. The knobs are near where the water softener is installed.
Loosen the screws in the metal rings holding the water line to the water softener and to the brine tank next to the water softener. Pull off the line.
Place the line in a shallow pan or bucket and pour enough distilled vinegar into the container to cover the hose. Let the line soak for an hour.
Thread the end of a fishing line through one end of the water line to the opposite side.
Tie the fishing line securely around a pipe cleaner. Pull the fishing line from the opposite side, dragging the pipe cleaner along with it, to clear the water line. Repeat with a fresh pipe cleaner until there is no discoloration on the pipe cleaner when it is pulled through the water line.
Reattach the line to the float assembly on the top of the water softener and to the brine tank. Tighten the screws in the metal rings on the line.
Plug in the power cord and twist the water cutoff knobs counterclockwise.