The answer is C because the middle term has to be no greater than -16 and no less than or equal to 2. So all you have to do is find how much terms for 'a' there is and make sure the inequality is true.
I found that the numbers from 1 to 6 makes 'a' true:
5-3(1)
5-3
=2
That makes the inequality true because it is greater than -16 and less than or EQUAL TO 2.
5-3(2)
5-6
=-1
That makes it true because it is greater than -16 and LESS THAN or equal to 2.
5-3(3)
5-9
=-4
That makes it true because it is greater than -16 and LESS THAN or equal to 2.
5-3(4)
5-12
=-7
That makes it true because it is greater than -16 and LESS THAN or equal to 2.
5-3(5)
5-15
=-10
That makes it true because it is greater than -16 and LESS THAN or equal to 2.
5-3(6)
5-18
=-13
That makes it true because it is greater than -16 and LESS THAN or equal to 2.
Here we can try 7, but the answer for that is equal to -16 and that can't work because -16 is not greater than -16, it's equal to:
5-3(7)
5-21
=-16
So to answer your question for what is the difference between the greatest and least value for 'a', the answer would be C because the greatest value is 6 and the least value is 1, so 6-1 is equal to 5.
Hope this helps!
:)
