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

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 distributive property to expand each term and then combine like terms.

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

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

3. Combine the results from step 1 and step 2: \[ 9k + 3 + 5k - 10 \]

4. Combine like terms:

   • Combine \(9k\) and \(5k\): \[ 9k + 5k = 14k \]
   • Combine \(3\) and \(-10\): \[ 3 - 10 = -7 \]

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

Thus, the simplified expression is: \[ \boxed{14k - 7} \]