Question

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

Answer 1

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

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

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

3. **Combine the results from both distributions:**
\[
9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) = (9k + 3) + (5k - 10)
\]

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

The simplified expression is:
\[
14k - 7
\]

Thus, the result of the expression \( 9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) \) is:
\[
\boxed{14k - 7}
\]