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Here’s the properties of operation to add 9 ( k+ 1/3) + 10 (1/2k - 1)

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To simplify the given expression, we will apply the distributive property of multiplication over addition/subtraction:

9(k + 1/3) + 10(1/2k - 1)

= 9 * k + 9 * (1/3) + 10 * (1/2k) + 10 * (-1)

= 9k + 3/3 + 10/2k - 10

= 9k + 1 + 5k - 10

= (9k + 5k) + (1 - 10)

= 14k - 9
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