Question

Question

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

14k+13
14 k plus 13

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

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

14k−7

Answer 1

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

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

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

Now combine the results: \[ (9k + 3) + (5k - 10) \]

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

Thus, the final answer is: \[ \boxed{14k - 7} \]