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

Question

.(1 point)
Responses

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

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

14k+13

Answer 1

To simplify the expression \( 9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) \), we will first distribute the terms.

1. Distribute \( 9 \) into \( (k + \frac{1}{3}) \): \[ 9(k + \frac{1}{3}) = 9k + 9 \cdot \frac{1}{3} = 9k + 3 \]

2. Distribute \( 10 \) into \( (\frac{1}{2}k - 1) \): \[ 10(\frac{1}{2}k - 1) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10 \]

3. Now combine the results from steps 1 and 2: \[ 9k + 3 + 5k - 10 \]

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

So, the simplified expression is: \[ 14k - 7 \]

The correct response is: 14k − 7.