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Simplifying 2(k + 9) + -1(5 + 3k) = -2k Reorder the terms: 2(9 + k) + -1(5 + 3k) = -2k (9 * 2 + k * 2) + -1(5 + 3k) = -2k (18 + 2k) + -1(5 + 3k) = -2k 18 + 2k + (5 * -1 + 3k * -1) = -2k 18 + 2k + (-5 + -3k) = -2k Reorder the terms: 18 + -5 + 2k + -3k = -2k Combine like terms: 18 + -5 = 13 13 + 2k + -3k = -2k Combine like terms: 2k + -3k = -1k 13 + -1k = -2k Solving 13 + -1k = -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. 13 + -1k + 2k = -2k + 2k Combine like terms: -1k + 2k = 1k 13 + 1k = -2k + 2k Combine like terms: -2k + 2k = 0 13 + 1k = 0 Add '-13' to each side of the equation. 13 + -13 + 1k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 1k = 0 + -13 1k = 0 + -13 Combine like terms: 0 + -13 = -13 1k = -13 Divide each side by '1'. k = -13 Simplifying k = -13
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