You are very wrong on just about all of that. Bicycles and mopeds are both required to stay to the right of the furthest right hand lane. A motorcycle can take a whole lane as well as legally ride two abreast.
No person shall operate a motorcycle or moped upon a highway or public vehicular area unless the operator and all passengers thereon wear safety helmets of a type approved by the Commissioner of Motor Vehicles
• A moped should travel using the right–hand side of the lane - To pass a moped, you must stay at least two feet to the left.
• The same DWI laws that apply to the drivers of other motor vehicles also apply to moped operators
• Stay out of traffic, as much as possible.
• Do not share lanes with other vehicles.
• Make sure other drivers can see you - wear light or brightly colored clothing.
• At an intersection, never "squeeze" between parked cars and moving traffic.
• If possible, install electric turn signals on your moped. Otherwise, be sure to use hand signals when you turn or stop.
• Failure to wear helmet, or having too many passengers, on a motorcycle or moped will result in a fine from $25 to $75.
And for bicycles:
In North Carolina, the bicycle has the legal status of a vehicle. This means that bicyclists have full
rights and responsibilities on the roadway and are subject to the regulations governing the
operation of a motor vehicle. North Carolina traffic laws require bicyclists to:
• Ride on the right in the same direction as other traffic
• Obey all traffic signs and signals
• Use hand signals to communicate intended movements
• Equip their bicycles with a front lamp visible from 300 feet and a rear reflector that is visible from a distance of 200 feet when riding at night.
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