The correct situations with matching inequality are:
c<10 The bag contains fewer than 10 carrots.
Explanation: Let the number of carrots be = c and given is there are fewer than 10 carrots in the bag, so c<10
c>10 Catherine biked farther than 10 miles.
Explanation: Let the miles be represented by 'c' so Catherine biked more than 10 miles, so c>10
c<20 The chair is shorter than 20 in.
Explanation: Let the height of the chair be = c . As it is shorter than or less than 20 so c<20
c>20 Carlos scored over 20 points.
Explanation: Let the points scored be =c and as Carlos scored over 20 points or more than 20, so c>20