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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 = -10 -10 + -27k + -84k = 1 + 10k + -11 + -6k Combine like terms: -27k + -84k = -111k -10 + -111k = 1 + 10k + -11 + -6k Reorder the terms: -10 + -111k = 1 + -11 + 10k + -6k Combine like terms: 1 + -11 = -10 -10 + -111k = -10 + 10k + -6k Combine like terms: 10k + -6k = 4k -10 + -111k = -10 + 4k Add '10' to each side of the equation. -10 + 10 + -111k = -10 + 10 + 4k Combine like terms: -10 + 10 = 0 0 + -111k = -10 + 10 + 4k -111k = -10 + 10 + 4k Combine like terms: -10 + 10 = 0 -111k = 0 + 4k -111k = 4k Solving -111k = 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. -111k + -4k = 4k + -4k Combine like terms: -111k + -4k = -115k -115k = 4k + -4k Combine like terms: 4k + -4k = 0 -115k = 0 Divide each side by '-115'. k = 0 Simplifying k = 0
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