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Simplifying -3(1 + -9k) + -7(12k + -1) = 1 + 10k + -11 + -6k (1 * -3 + -9k * -3) + -7(12k + -1) = 1 + 10k + -11 + -6k (-3 + 27k) + -7(12k + -1) = 1 + 10k + -11 + -6k Reorder the terms: -3 + 27k + -7(-1 + 12k) = 1 + 10k + -11 + -6k -3 + 27k + (-1 * -7 + 12k * -7) = 1 + 10k + -11 + -6k -3 + 27k + (7 + -84k) = 1 + 10k + -11 + -6k Reorder the terms: -3 + 7 + 27k + -84k = 1 + 10k + -11 + -6k Combine like terms: -3 + 7 = 4 4 + 27k + -84k = 1 + 10k + -11 + -6k Combine like terms: 27k + -84k = -57k 4 + -57k = 1 + 10k + -11 + -6k Reorder the terms: 4 + -57k = 1 + -11 + 10k + -6k Combine like terms: 1 + -11 = -10 4 + -57k = -10 + 10k + -6k Combine like terms: 10k + -6k = 4k 4 + -57k = -10 + 4k Solving 4 + -57k = -10 + 4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4k' to each side of the equation. 4 + -57k + -4k = -10 + 4k + -4k Combine like terms: -57k + -4k = -61k 4 + -61k = -10 + 4k + -4k Combine like terms: 4k + -4k = 0 4 + -61k = -10 + 0 4 + -61k = -10 Add '-4' to each side of the equation. 4 + -4 + -61k = -10 + -4 Combine like terms: 4 + -4 = 0 0 + -61k = -10 + -4 -61k = -10 + -4 Combine like terms: -10 + -4 = -14 -61k = -14 Divide each side by '-61'. k = 0.2295081967 Simplifying k = 0.2295081967
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