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Simplifying 7k + -1(9k + -16) = 14 + -1(19 + -1k) Reorder the terms: 7k + -1(-16 + 9k) = 14 + -1(19 + -1k) 7k + (-16 * -1 + 9k * -1) = 14 + -1(19 + -1k) 7k + (16 + -9k) = 14 + -1(19 + -1k) Reorder the terms: 16 + 7k + -9k = 14 + -1(19 + -1k) Combine like terms: 7k + -9k = -2k 16 + -2k = 14 + -1(19 + -1k) 16 + -2k = 14 + (19 * -1 + -1k * -1) 16 + -2k = 14 + (-19 + 1k) Combine like terms: 14 + -19 = -5 16 + -2k = -5 + 1k Solving 16 + -2k = -5 + 1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1k' to each side of the equation. 16 + -2k + -1k = -5 + 1k + -1k Combine like terms: -2k + -1k = -3k 16 + -3k = -5 + 1k + -1k Combine like terms: 1k + -1k = 0 16 + -3k = -5 + 0 16 + -3k = -5 Add '-16' to each side of the equation. 16 + -16 + -3k = -5 + -16 Combine like terms: 16 + -16 = 0 0 + -3k = -5 + -16 -3k = -5 + -16 Combine like terms: -5 + -16 = -21 -3k = -21 Divide each side by '-3'. k = 7 Simplifying k = 7
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