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To add the given algebraic expressions, we need to simplify each term first:
9(k + 1/3) + 10(1/2k - 1)
= 9k + 9(1/3) + 10(1/2k) - 10(1)
= 9k + 3 + 5k - 10
= 14k - 7
Therefore, the sum is 14k - 7 in simplified form.