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Simplifying (12k + 3) + (6 + -2k) + -1(8k + -4) = 0 Reorder the terms: (3 + 12k) + (6 + -2k) + -1(8k + -4) = 0 Remove parenthesis around (3 + 12k) 3 + 12k + (6 + -2k) + -1(8k + -4) = 0 Remove parenthesis around (6 + -2k) 3 + 12k + 6 + -2k + -1(8k + -4) = 0 Reorder the terms: 3 + 12k + 6 + -2k + -1(-4 + 8k) = 0 3 + 12k + 6 + -2k + (-4 * -1 + 8k * -1) = 0 3 + 12k + 6 + -2k + (4 + -8k) = 0 Reorder the terms: 3 + 6 + 4 + 12k + -2k + -8k = 0 Combine like terms: 3 + 6 = 9 9 + 4 + 12k + -2k + -8k = 0 Combine like terms: 9 + 4 = 13 13 + 12k + -2k + -8k = 0 Combine like terms: 12k + -2k = 10k 13 + 10k + -8k = 0 Combine like terms: 10k + -8k = 2k 13 + 2k = 0 Solving 13 + 2k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 2k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2k = 0 + -13 2k = 0 + -13 Combine like terms: 0 + -13 = -13 2k = -13 Divide each side by '2'. k = -6.5 Simplifying k = -6.5
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