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Simplifying -14 = 2(6 + -1k) + 6(7 + 6k) -14 = (6 * 2 + -1k * 2) + 6(7 + 6k) -14 = (12 + -2k) + 6(7 + 6k) -14 = 12 + -2k + (7 * 6 + 6k * 6) -14 = 12 + -2k + (42 + 36k) Reorder the terms: -14 = 12 + 42 + -2k + 36k Combine like terms: 12 + 42 = 54 -14 = 54 + -2k + 36k Combine like terms: -2k + 36k = 34k -14 = 54 + 34k Solving -14 = 54 + 34k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-34k' to each side of the equation. -14 + -34k = 54 + 34k + -34k Combine like terms: 34k + -34k = 0 -14 + -34k = 54 + 0 -14 + -34k = 54 Add '14' to each side of the equation. -14 + 14 + -34k = 54 + 14 Combine like terms: -14 + 14 = 0 0 + -34k = 54 + 14 -34k = 54 + 14 Combine like terms: 54 + 14 = 68 -34k = 68 Divide each side by '-34'. k = -2 Simplifying k = -2
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