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Simplifying 4(k + 7) + 5(k + -2) = 0 Reorder the terms: 4(7 + k) + 5(k + -2) = 0 (7 * 4 + k * 4) + 5(k + -2) = 0 (28 + 4k) + 5(k + -2) = 0 Reorder the terms: 28 + 4k + 5(-2 + k) = 0 28 + 4k + (-2 * 5 + k * 5) = 0 28 + 4k + (-10 + 5k) = 0 Reorder the terms: 28 + -10 + 4k + 5k = 0 Combine like terms: 28 + -10 = 18 18 + 4k + 5k = 0 Combine like terms: 4k + 5k = 9k 18 + 9k = 0 Solving 18 + 9k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + 9k = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 9k = 0 + -18 9k = 0 + -18 Combine like terms: 0 + -18 = -18 9k = -18 Divide each side by '9'. k = -2 Simplifying k = -2
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