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

Question

9
(
𝑘
+
1
3
)
+
10
(
1
2
𝑘
−
1
)
.(1 point)
Responses

14k−7
14
𝑘
−
7
14 k minus 7

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

14k+13
14
𝑘
+
13
14 k plus 13

1912k−2/3

Answer 1

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

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

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

3. Now we can combine the results: \[ 9k + 3 + 5k - 10 \]

4. Combine like terms - first for \( k \) terms: \[ 9k + 5k = 14k \]

5. Now, combine the constant terms: \[ 3 - 10 = -7 \]

Putting it all together, we get: \[ 14k - 7 \]

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