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Simplifying 5(7 + k) + 2(2 + -2k) = 0 (7 * 5 + k * 5) + 2(2 + -2k) = 0 (35 + 5k) + 2(2 + -2k) = 0 35 + 5k + (2 * 2 + -2k * 2) = 0 35 + 5k + (4 + -4k) = 0 Reorder the terms: 35 + 4 + 5k + -4k = 0 Combine like terms: 35 + 4 = 39 39 + 5k + -4k = 0 Combine like terms: 5k + -4k = 1k 39 + 1k = 0 Solving 39 + 1k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + 1k = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 1k = 0 + -39 1k = 0 + -39 Combine like terms: 0 + -39 = -39 1k = -39 Divide each side by '1'. k = -39 Simplifying k = -39
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