Question

Under which situations is w – z always negative?

O w and z are both positive.
w and z are both negative.
O w is positive and z is negative.
O w is negative and z is positive.

Answer 1

w - z is always negative when w is negative and z is positive, as this situation implies subtracting a positive number from a negative one, which results in a greater negative value.

Step-by-step explanation:

To determine under which situations w - z is always negative, it's important to understand how the signs of numbers influence the result of their subtraction. We need to evaluate each scenario given:

• If both w and z are positive, w - z could be either positive or negative, depending on which is larger.
• If both w and z are negative, w - z could also be positive or negative, again depending on which absolute value is larger.
• If w is positive and z is negative, then w - z is always positive because you're effectively adding the absolute value of z to w.
• If w is negative and z is positive, w - z is always negative because you're subtracting a positive number from a negative number, moving further into negative territory.

Therefore, the answer to the question is that w - z is always negative when w is negative and z is positive.