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.