Use the properties of operations to add 9 (k+1/3)+10 (1/2k-1)
A. 19 1/2k-2/3
B. 14k+13
C. 14k -7
D. 14k-2/3
To add the expressions 9 (k+1/3) and 10 (1/2k-1), we need to distribute the 9 and the 10 separately:
Distributing 9:
9(k) + 9(1/3) = 9k + 3
Distributing 10:
10(1/2k) + 10(-1) = 5/k - 10
Now we can combine like terms by adding the two expressions:
(9k + 3) + (5/k - 10)
Next, let's get a common denominator for the fraction:
(9k + 3) + ((5 - 10k)/k)
To combine the fractions, we need to find a common denominator of k:
(9k + 3) + ((5 - 10k)/k) = (9k + 3k + 5 - 10k) / k
Simplifying the numerator:
(9k + 3k + 5 - 10k) = (12k - 10k + 5) = 14k + 5
Putting it all together, we have:
(9k + 3k + 5 - 10k) / k = (14k + 5) / k
Therefore, the correct answer is option:
B. 14k + 13