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

Question

.(1 point)
Responses

14k−23
14 k minus Start Fraction 2 over 3 End Fraction

14k+13
14 k plus 13

1912k−23
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

14k−7
14 k minus 7
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Answer 1

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.

1. Distribute the coefficients:

\[ 9\left(k+\frac{1}{3}\right) = 9k + 3 \]

\[ 10\left(\frac{1}{2}k-1\right) = 5k - 10 \]

2. Combine the results:

\[ 9k + 3 + 5k - 10 \]

3. Combine like terms:

\[ (9k + 5k) + (3 - 10) = 14k - 7 \]

Thus, the final simplified expression is:

\[ 14k - 7 \]

The correct response is:

14k−7