Final answer:
The expression 7+5(3c-1) simplifies to 2+15c by using the distributive property and combining like terms. To ensure the result is reasonable, verify each step was correctly executed.
Step-by-step explanation:
To simplify the expression 7+5(3c-1), first apply the distributive property to multiply 5 by both 3c and -1. This operation gives you 5 × 3c which is 15c, and 5 × (-1) which is -5. Adding these products to 7 results in the simplified expression: 7 + 15c - 5.
Combining the like terms 7 and -5 gives you 2 + 15c. Therefore, the expression 7 + 5(3c - 1) simplifies to 2 + 15c.
Lastly, a quick check to make sure this is reasonable would confirm that the multiplication and addition were done correctly, and indeed, 2 + 15c is a correct simplification of the given expression.