If 1≥ y ≥0 and z ≤ -2 , then which of the following cannot be the valu

We are given that 1 ≥ y ≥ 0 and z ≤ -2, and we need to determine which of the answer choices CANNOT be equal to y - z.

A) 3

If y = 1 and z = -2, then y - z = 1 - (-2) = 3.

B) 2.75

If y = 0.75 and z = -2, then y - z = 0.75 - (-2) = 2.75.

C) 2.5

If y = 0.5 and z = -2, then y - z = 0.5 - (-2) = 2.5.

D) 2

If y = 0 and z = -2, then y - z = 0 - (-2) = 2.

E) We see that there is no way for y - z to equal 1.5. Recall that y is a number between 0 and 1 (inclusive), and z is a number less than or equal to -2. Therefore, y minus z (i.e., y minus -2) is equivalent to y plus 2. When a number between 0 and 1 (inclusive) is added to 2, the sum will be at least 2.

Alternate Solution:

Since z ≤ -2, multiplying each side by -1 (and reversing the inequality sign), we have -z ≥ 2. Also, y ≥ 0; adding the two inequalities together, we have y - z ≥ 2. Among the choices, only 1.5 does not satisfy this inequality.

Answer: E