Answer:
1. Smallest integer value of x: 2
2. largest integer value of y: 8
3. greatest possible value of x-y: 12
4. smallest possible value of x-y: 1
5. greatest possible value of x/y: 8
Explanation:
Inequalities are
3 < x ≤ 8
- 4 ≤ y ≤ 1
1. Since 3 < x which is the same as saying x > 3 , x cannot be 3 but any real number above 3. The next lower integer is 2. So 2 is the smallest integer value of x
2. The largest integer value of x is 8 which is determined by the ≤ signe. This means that x is less than or equal to 3
3. To find the greatest possible value of x - y, take the largest value of x and subtract the smallest value of y. Smallest value of y = -4. So the answer is 8 - (-4) = 8 + 4 = 12
4. Smallest possible value of x - y = smallest x value - largest y value = 2 - 1 = 1. This is only if we are considering integer values which is what I presume the question implies
5. greatest possible value of x/y. This is tricky because the smallest y is negative. So we have to find largest x/y at the interval edges and see which one is the largest
8/-4 = -2 and 8/1 = 8
So largest x/y value is 8