Now, we can substitute each of the integers for b and check the value of the numerator.
b
b-5/a
Simplify
- 2
- 2-5/a
- 7/a
5
5-5/a
0/a
9
9-5/a
4/a
10
10-5/a
5/a
Right away we can disregard - 2 and 5 as values of b. Inputting these values resulted in fractions that will not give a positivequotient when dividing by any of the remaining integers. We only have two options now.
b=9 or b=10
From the numbers available, 4 is only divisible by - 2, but this would result in a negative quotient, so we can disregard b=9. Dividing 5 by 5 equals 1, a positive integer! Therefore, a=5.
When a= 5 and b=10, x is a positive integer.
b From Part A, we know that substituting the various values for b gives us the following fractions.
- 7/a, 0/a, 4/a, and 5/a
Again, we can disregard the first two fractions, they will not give us a negative integer when substituting any of the remaining values for a. This leaves us with two options.
b=9 or b=10
Since we are looking for a negative quotient, we are going to need a negative denominator, which must be a=-2.
The only numerator that is divisible by - 2 is 4. Therefore b=9.
