At least two copies of the tax budget estimates shall be placed on file in the office of the Director of Finance on or before June 1 for public inspection. Notice that they are available for that purpose shall be given by publication in a newspaper of general circulation in the City not later than June 5 of each year. The Council shall hold at least one public hearing on the tax budget of which notice shall be given by publication as above not less than ten days prior to the hearing.