Question

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

14k - 7

14k - 2/3

19 1/2k - 2/3

14k + 13

Answer 1

To add the expression \( 9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) \), we will use the distributive property and then combine like terms. Here's the step-by-step breakdown:

1. **Distribute the 9 and the 10**:

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

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

2. **Combine the results**:

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

3. **Combine like terms**:

- Combine the \( k \) terms:
\[
9k + 5k = 14k
\]

- Combine the constant terms:
\[
3 - 10 = -7
\]

4. **Put it all together**:

\[
14k - 7
\]

So, the final result is:

\[
\boxed{14k - 7}
\]