9(k + 1/3) + 10(1/2k - 1)

To simplify the expression 9(k + 1/3) + 10(1/2k - 1), we first distribute the 9 and the 10 to each term in the parentheses:

9(k) + 9(1/3) + 10(1/2k) - 10(1)

This simplifies to:

9k + 3 + 10(1/2k) - 10

Next, we simplify the expression 10(1/2k):

10(1/2k) = 10/2k = 5/k

Therefore, the expression becomes:

9k + 3 + 5/k - 10

Combining like terms, we get:

9k + 5/k - 7