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

Question

Responses

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
14 k minus Start Fraction 2 over 3 End Fraction

14k−7
14 k minus 7

14k+13
14 k plus 13

Answer 1

To simplify the expression \( 9\left(k + \frac{1}{3}\right) + 10\left(\frac{1}{2}k - 1\right) \), we can follow these steps:

1. Distribute the constants: \[ 9\left(k + \frac{1}{3}\right) = 9k + 9\cdot\frac{1}{3} = 9k + 3 \] \[ 10\left(\frac{1}{2}k - 1\right) = 10\cdot\frac{1}{2}k - 10\cdot1 = 5k - 10 \]

2. Combine the results from both distributions: \[ 9k + 3 + 5k - 10 \]

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

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

This corresponds to the response \( 14k - 7 \).