Use the properties of operations to add 9(k+1/3) +10(1/2k−1).
A. 14k - 2/3
B. 19 1/2k - 2/3
C. 14k + 13
D. 14k - 7
To add 9(k+1/3) + 10(1/2k-1), we must use the distributive property of multiplication over addition.
First, distribute the 9 to both terms inside the parentheses:
9 * k = 9k
9 * 1/3 = 3
Next, distribute the 10 to both terms inside the parentheses:
10 * 1/2k = 5k
10 * -1 = -10
Now, we can combine the like terms:
9k + 3 + 5k - 10
Combine the k terms:
(9k + 5k) + (3 - 10) = 14k - 7
So the answer is D. 14k - 7.