To add 9(k + 1/3) + 10(1/2k - 1), we can use the distributive property to simplify.
First, we distribute 9 to both terms inside the first parentheses: 9k + 9/3
Next, we distribute 10 to both terms inside the second parentheses: 10/2k - 10
Simplifying the fractions, 9/3 = 3 and 10/2 = 5.
Now we can combine like terms: 9k + 3 + 5k - 10
Combining like terms, we get: 14k - 7
Therefore, the simplified expression is 14k - 7.
The correct answer is C. 14k - 7.