To simplify the expression \( 9\left(k+\frac{1}{3}\right)+10\left(\frac{1}{2}k-1\right) \), we will use the properties of operations.
- Distribute the coefficients:
\[ 9\left(k+\frac{1}{3}\right) = 9k + 3 \]
\[ 10\left(\frac{1}{2}k-1\right) = 5k - 10 \]
- Combine the results:
\[ 9k + 3 + 5k - 10 \]
- Combine like terms:
\[ (9k + 5k) + (3 - 10) = 14k - 7 \]
Thus, the final simplified expression is:
\[ 14k - 7 \]
The correct response is:
14k−7