To simplify the expression \( 9(k+13) + 10(12k-1) \), we will use the distributive property of operations.
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Distribute the 9 into the first term: \[ 9(k + 13) = 9k + 9 \cdot 13 = 9k + 117 \]
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Distribute the 10 into the second term: \[ 10(12k - 1) = 10 \cdot 12k + 10 \cdot (-1) = 120k - 10 \]
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Combine both results: \[ 9(k+13) + 10(12k-1) = (9k + 117) + (120k - 10) \]
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Combine like terms:
- Combine the \( k \) terms: \( 9k + 120k = 129k \)
- Combine the constants: \( 117 - 10 = 107 \)
Putting it all together, we have: \[ 9(k+13) + 10(12k-1) = 129k + 107 \]
Thus, the simplified expression is: \[ \boxed{129k + 107} \]
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