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

14k−7
14 k minus 7

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

Answer 1

To simplify the expression \( 9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) \), we can use the distributive property.

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

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

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

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

Putting it all together: \[ 14k - 7. \]

Therefore, the final answer is: 14k - 7.