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

Question

.(1 point)
Responses

14k−23
14 k minus Start Fraction 2 over 3 End Fraction

14k+13
14 k plus 13

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

14k−7
14 k minus 7
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Answer 1

To simplify the expression \( 9(k + 13) + 10(12k - 1) \) using the properties of operations, follow these steps:

1. Distribute \( 9 \) and \( 10 \) to the terms inside the parentheses: \[ 9(k + 13) = 9k + 117 \] \[ 10(12k - 1) = 120k - 10 \]

2. Combine the results: \[ 9k + 117 + 120k - 10 \]

3. Combine like terms \( 9k + 120k \) and \( 117 - 10 \): \[ (9k + 120k) + (117 - 10) = 129k + 107 \]

Thus, the simplified expression is \( 129k + 107 \), which does not match any of the provided options. It seems there may have been an expectation for a specific form, or there may be a typographical error in the options provided.

If the options somehow do not represent the correct simplification, the process of simplification is as above.