Question

For all the nonzero values of a and b, the value of which of the following expressions is always negative?

a) A - b
b) -a - b
c) |a| + |b|
d) |a| - |b|

Answer 1

For all nonzero values of a and b, the expression that is always negative is -a - b, because both terms are negative for nonzero values of a and b.

Step-by-step explanation:

To determine which of the given expressions is always negative for all nonzero values of a and b, we must consider the nature of each expression:

• Expression (a), which is A - b, can be positive, negative or zero, depending on the values of a and b.
• Expression (b), which is -a - b, is always negative because both -a and -b are negative for nonzero values of a and b.
• Expression (c), which is |a| + |b|, is always positive since absolute values are never negative.
• Expression (d), which is |a| - |b|, can be positive, negative, or zero, depending on the relative sizes of |a| and |b|.

Thus, expression (b) -a - b is always negative for all nonzero values of a and b.