Answer
$6$ different routes;
shortest route: direct route from Portland to Tucson;
$x\ge973$
Work Step by Step
A possible route goes directly from Portland to Tucson.
A second possible route goes from Portland-San Diego-Tucson.
A third possible route goes from Portland-San Diego-Las Vegas-Tucson.
A fourth possible route goes from Portland-San Diego-Boise-Seattle-Las Vegas-Tucson.
A fifth possible route goes from Portland-Las Vegas-Tucson.
A sixth possible route goes from Portland-Las Vegas-Seattle-Boise-San Diego-Tucson.
Therefore, there is a total of $6$ routes from Portland to Tucson.
The shortest route is the direct route from Portland to Tucson with a distance of $973$ miles.
Since the shortest route is $973$ miles, then an inequality that represents the mileage of any route from Portland to Tucson is
$$
x\ge973
.$$
