Use the properties of operations to add 9(k+13)+10(12k−1)

Question

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

14k+13
14
𝑘
+
13
14 k plus 13

14k−7
14
𝑘
−
7
14 k minus 7

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

14k−23

Answer 1

To simplify the expression \( 9(k + 13) + 10(12k - 1) \), we'll use the distributive property.

1. Distribute the \( 9 \) in \( 9(k + 13) \): \[ 9k + 117 \]

2. Distribute the \( 10 \) in \( 10(12k - 1) \): \[ 120k - 10 \]

3. Now, combine the two results: \[ (9k + 117) + (120k - 10) \]

4. Combine like terms:

   • Combine \( 9k \) and \( 120k \): \[ 9k + 120k = 129k \]
   • Combine \( 117 \) and \( -10 \): \[ 117 - 10 = 107 \]

5. Thus, the final simplified expression is: \[ 129k + 107 \]

Now let's see how this matches the options presented:

• 14k + 13
• 14k − 7
• 1912k − 23
• 14k − 23

None of the provided response options match the correct simplification of \( 129k + 107 \). It appears there may have been an error in the answer choices provided. The correct simplified expression is \( 129k + 107 \).