The City Council may provide by ordinance for boards of adjustment or appeal which shall be given authority to hear and determine appeals from administrative rulings of City officials or inspectors, or to hear and resolve citizen complaints and grievances in general, with such jurisdiction and power as may be prescribed by ordinance.

The membership, terms, and eligibility for such boards shall be determined by the City Council. The members of said boards shall be appointed by the Mayor with the approval of the City Council, and removed by the Mayor with the approval of a majority plus one of all members of the City Council.