Question

9(k+1/3)+10(1/2k−1)

Answer 1

You interpreted 10(1/2k−1) as 10(1/(2k) -1) = 5/k - 10

I'm pretty sure they meant
9(k+1/3)+10(1/2 k−1) = 9k+3+5k-10 = 14k-7

Answer 2

9(k+1/3) + 10(1/2k-1)
= 9k + 3 + 10(1/2k-1)
= 9k + 3 + 10/2k - 10
= 9k + 3 + 5/k - 10
= 9k + 5/k - 7

Answer 3

Apologies for the incorrect interpretation. You are right.

9(k+1/3) + 10(1/2k-1)
= 9k + 3 + 10(1/2k) - 10
= 9k + 3 + 5k - 10
= 14k - 7