Final answer:
Using the distributive property, the expression -1/6 (-30-42c) simplifies to 5 + 7c, because multiplying a negative by a negative yields a positive result for both terms.
Step-by-step explanation:
To simplify the expression -1/6 (-30-42c) using the distributive property, we multiply -1/6 by each term inside the parentheses.
The distributive property states that a(b + c) = ab + ac. Applying this rule here, we have:
-1/6 * (-30) = 5 (because a negative times a negative equals a positive)
-1/6 * (-42c) = 7c (again, a negative times a negative equals a positive)
So the simplified expression is 5 + 7c.