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Simplifying 27 + 2 + -4 + -1(k + -3) = -16 + -1(3k + -4) Reorder the terms: 27 + 2 + -4 + -1(-3 + k) = -16 + -1(3k + -4) 27 + 2 + -4 + (-3 * -1 + k * -1) = -16 + -1(3k + -4) 27 + 2 + -4 + (3 + -1k) = -16 + -1(3k + -4) Combine like terms: 27 + 2 = 29 29 + -4 + 3 + -1k = -16 + -1(3k + -4) Combine like terms: 29 + -4 = 25 25 + 3 + -1k = -16 + -1(3k + -4) Combine like terms: 25 + 3 = 28 28 + -1k = -16 + -1(3k + -4) Reorder the terms: 28 + -1k = -16 + -1(-4 + 3k) 28 + -1k = -16 + (-4 * -1 + 3k * -1) 28 + -1k = -16 + (4 + -3k) Combine like terms: -16 + 4 = -12 28 + -1k = -12 + -3k Solving 28 + -1k = -12 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. 28 + -1k + 3k = -12 + -3k + 3k Combine like terms: -1k + 3k = 2k 28 + 2k = -12 + -3k + 3k Combine like terms: -3k + 3k = 0 28 + 2k = -12 + 0 28 + 2k = -12 Add '-28' to each side of the equation. 28 + -28 + 2k = -12 + -28 Combine like terms: 28 + -28 = 0 0 + 2k = -12 + -28 2k = -12 + -28 Combine like terms: -12 + -28 = -40 2k = -40 Divide each side by '2'. k = -20 Simplifying k = -20
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