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Simplifying 1 = 8(6k + 2) + -3(6k + 5) Reorder the terms: 1 = 8(2 + 6k) + -3(6k + 5) 1 = (2 * 8 + 6k * 8) + -3(6k + 5) 1 = (16 + 48k) + -3(6k + 5) Reorder the terms: 1 = 16 + 48k + -3(5 + 6k) 1 = 16 + 48k + (5 * -3 + 6k * -3) 1 = 16 + 48k + (-15 + -18k) Reorder the terms: 1 = 16 + -15 + 48k + -18k Combine like terms: 16 + -15 = 1 1 = 1 + 48k + -18k Combine like terms: 48k + -18k = 30k 1 = 1 + 30k Add '-1' to each side of the equation. 1 + -1 = 1 + -1 + 30k Combine like terms: 1 + -1 = 0 0 = 1 + -1 + 30k Combine like terms: 1 + -1 = 0 0 = 0 + 30k 0 = 30k Solving 0 = 30k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-30k' to each side of the equation. 0 + -30k = 30k + -30k Remove the zero: -30k = 30k + -30k Combine like terms: 30k + -30k = 0 -30k = 0 Divide each side by '-30'. k = 0 Simplifying k = 0
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