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Simplifying -9(1 + 12k) + 5(3k + 4) = -82 (1 * -9 + 12k * -9) + 5(3k + 4) = -82 (-9 + -108k) + 5(3k + 4) = -82 Reorder the terms: -9 + -108k + 5(4 + 3k) = -82 -9 + -108k + (4 * 5 + 3k * 5) = -82 -9 + -108k + (20 + 15k) = -82 Reorder the terms: -9 + 20 + -108k + 15k = -82 Combine like terms: -9 + 20 = 11 11 + -108k + 15k = -82 Combine like terms: -108k + 15k = -93k 11 + -93k = -82 Solving 11 + -93k = -82 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -93k = -82 + -11 Combine like terms: 11 + -11 = 0 0 + -93k = -82 + -11 -93k = -82 + -11 Combine like terms: -82 + -11 = -93 -93k = -93 Divide each side by '-93'. k = 1 Simplifying k = 1
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