Use the properties of operations to add 9(k+1/3)+10(1/2k−1)

Question

.(1 point)
Responses

14k−7
14 k minus 7

14k+13
14 k plus 13

19 1/2k−2/3
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

14k−2/3

Answer 1

To simplify the expression \( 9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) \), we will distribute and then combine like terms.

1. Distribute \( 9 \) in the first term: \[ 9(k + \frac{1}{3}) = 9k + 9 \times \frac{1}{3} = 9k + 3 \]

2. Distribute \( 10 \) in the second term: \[ 10(\frac{1}{2}k - 1) = 10 \times \frac{1}{2}k - 10 \times 1 = 5k - 10 \]

3. Now, combine the two results: \[ 9k + 3 + 5k - 10 \]

4. Combine like terms: \[ (9k + 5k) + (3 - 10) = 14k - 7 \]

Thus, the final result is: \[ \boxed{14k - 7} \]