Question

Use the properties of operations to add 9(k+1/3)+10(1/2k−1).(1 point)
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 \( 14k - 7 \).