Final answer:
The sum of the expressions -1/2 (7z + 4) and 1/5 (5z - 15), after distributing and combining like terms, is -5z/2 - 5, which is not listed in the given options.
Step-by-step explanation:
The sum of -1/2 (7z + 4) plus 1/5 (5z - 15) involves two steps: distributing the fractions across each term within the parentheses, and then simplifying by combining like terms.
- Multiply -1/2 by each term inside the first set of parentheses: -1/2 × 7z = -7z/2 and -1/2 × 4 = -2.
- Multiply 1/5 by each term inside the second set of parentheses: 1/5 × 5z = z and 1/5 × -15 = -3.
- Combine like terms: -7z/2 + z can be combined by finding a common denominator, which is 2, resulting in -7z/2 + 2z/2 = -5z/2. Combine the constant terms: -2 - 3 = -5.
- The final simplified sum is: -5z/2 - 5.
This does not match with any of the given options A, B, C, or D. Therefore, the correct sum is not listed among the provided options.