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Simplifying 27 + -2 + -4 + -1(-1k + -3) = -16 + -1(3k + -4) Reorder the terms: 27 + -2 + -4 + -1(-3 + -1k) = -16 + -1(3k + -4) 27 + -2 + -4 + (-3 * -1 + -1k * -1) = -16 + -1(3k + -4) 27 + -2 + -4 + (3 + 1k) = -16 + -1(3k + -4) Combine like terms: 27 + -2 = 25 25 + -4 + 3 + 1k = -16 + -1(3k + -4) Combine like terms: 25 + -4 = 21 21 + 3 + 1k = -16 + -1(3k + -4) Combine like terms: 21 + 3 = 24 24 + 1k = -16 + -1(3k + -4) Reorder the terms: 24 + 1k = -16 + -1(-4 + 3k) 24 + 1k = -16 + (-4 * -1 + 3k * -1) 24 + 1k = -16 + (4 + -3k) Combine like terms: -16 + 4 = -12 24 + 1k = -12 + -3k Solving 24 + 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. 24 + 1k + 3k = -12 + -3k + 3k Combine like terms: 1k + 3k = 4k 24 + 4k = -12 + -3k + 3k Combine like terms: -3k + 3k = 0 24 + 4k = -12 + 0 24 + 4k = -12 Add '-24' to each side of the equation. 24 + -24 + 4k = -12 + -24 Combine like terms: 24 + -24 = 0 0 + 4k = -12 + -24 4k = -12 + -24 Combine like terms: -12 + -24 = -36 4k = -36 Divide each side by '4'. k = -9 Simplifying k = -9
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