tell whether this pair of expressions is equivalent

the quantity negative x minus eight divided by two and negative one half x plus negative four

Yes, the pair of expressions is equivalent.

The expression "negative x minus eight divided by two" can be represented as (-x - 8) / 2.

Simplifying this expression, we get -x / 2 - 8 / 2 = -x /2 - 4, which can also be expressed as -1/2x - 4.

Therefore, the expression "negative x minus eight divided by two" is equivalent to "negative one half x plus negative four".