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Simplifying 8(w + 5) + -1(6w + -1k) + 9k = 0 Reorder the terms: 8(5 + w) + -1(6w + -1k) + 9k = 0 (5 * 8 + w * 8) + -1(6w + -1k) + 9k = 0 (40 + 8w) + -1(6w + -1k) + 9k = 0 Reorder the terms: 40 + 8w + -1(-1k + 6w) + 9k = 0 40 + 8w + (-1k * -1 + 6w * -1) + 9k = 0 40 + 8w + (1k + -6w) + 9k = 0 Reorder the terms: 40 + 1k + 9k + 8w + -6w = 0 Combine like terms: 1k + 9k = 10k 40 + 10k + 8w + -6w = 0 Combine like terms: 8w + -6w = 2w 40 + 10k + 2w = 0 Solving 40 + 10k + 2w = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + 10k + -40 + 2w = 0 + -40 Reorder the terms: 40 + -40 + 10k + 2w = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 10k + 2w = 0 + -40 10k + 2w = 0 + -40 Combine like terms: 0 + -40 = -40 10k + 2w = -40 Add '-2w' to each side of the equation. 10k + 2w + -2w = -40 + -2w Combine like terms: 2w + -2w = 0 10k + 0 = -40 + -2w 10k = -40 + -2w Divide each side by '10'. k = -4 + -0.2w Simplifying k = -4 + -0.2w
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