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3 < x ≤ 8

-4 ≤ y ≤ 1

Find:
1. Smallest integer value of x
2. largest integer value of y
3. greatest possible value of x-y
4. smallest possible value of x-y
5. greatest possible value of x/y

User Kisinga
by
8.6k points

1 Answer

4 votes

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

User Martona
by
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