Final answer:
The expression 6c + 4d -c + 7d simplifies to 5c + 11d, by combining like terms c and d respectively.
Step-by-step explanation:
To simplify the algebraic expression 6c + 4d -c + 7d, we need to combine like terms. The terms 6c and -c are like terms because they both contain the variable c, and similarly 4d and 7d are like terms because they contain the variable d.
First, let's combine the c terms:
6c - c = 5c
Then, we combine the d terms:
4d + 7d = 11d
Now, we can write the simplified expression:
5c + 11d
After simplifying, we check to make sure this is reasonable by verifying that all like terms have been properly combined and no terms have been omitted, which they have.