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Simplifying k + -3(2 + -4k) = 7 + -1(8k + -9 + k) k + (2 * -3 + -4k * -3) = 7 + -1(8k + -9 + k) k + (-6 + 12k) = 7 + -1(8k + -9 + k) Reorder the terms: -6 + k + 12k = 7 + -1(8k + -9 + k) Combine like terms: k + 12k = 13k -6 + 13k = 7 + -1(8k + -9 + k) Reorder the terms: -6 + 13k = 7 + -1(-9 + 8k + k) Combine like terms: 8k + k = 9k -6 + 13k = 7 + -1(-9 + 9k) -6 + 13k = 7 + (-9 * -1 + 9k * -1) -6 + 13k = 7 + (9 + -9k) Combine like terms: 7 + 9 = 16 -6 + 13k = 16 + -9k Solving -6 + 13k = 16 + -9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9k' to each side of the equation. -6 + 13k + 9k = 16 + -9k + 9k Combine like terms: 13k + 9k = 22k -6 + 22k = 16 + -9k + 9k Combine like terms: -9k + 9k = 0 -6 + 22k = 16 + 0 -6 + 22k = 16 Add '6' to each side of the equation. -6 + 6 + 22k = 16 + 6 Combine like terms: -6 + 6 = 0 0 + 22k = 16 + 6 22k = 16 + 6 Combine like terms: 16 + 6 = 22 22k = 22 Divide each side by '22'. k = 1 Simplifying k = 1
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