Output values from all entries in a specific section EXCEPT those with a specific category id
You can get the entry IDs that have are related to the category and then exclude them from the all the entries.

{% set entryIdsWithCategory = 
craft.entries.section('driverPositions').relatedTo('7192').limit(null).ids() %}

{% set entryIdsWithoutCategory = craft.entries.section('driverPositions').limit(null).ids()|without(entryIdsWithCategory) %}

{% set entries = craft.entries.section('businesses').limit(null).id(entryIdsWithoutCategory).order('state, city') %}

{% for entry in entries %}
    &lt;option value="{{entry.url}}"&gt;{{ entry.state }} - {{ entry.city }}&lt;/option&gt;
{% endfor %}