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Simplifying -1(8k + 2) = 10(1 + -3k) + 3 Reorder the terms: -1(2 + 8k) = 10(1 + -3k) + 3 (2 * -1 + 8k * -1) = 10(1 + -3k) + 3 (-2 + -8k) = 10(1 + -3k) + 3 -2 + -8k = (1 * 10 + -3k * 10) + 3 -2 + -8k = (10 + -30k) + 3 Reorder the terms: -2 + -8k = 10 + 3 + -30k Combine like terms: 10 + 3 = 13 -2 + -8k = 13 + -30k Solving -2 + -8k = 13 + -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. -2 + -8k + 30k = 13 + -30k + 30k Combine like terms: -8k + 30k = 22k -2 + 22k = 13 + -30k + 30k Combine like terms: -30k + 30k = 0 -2 + 22k = 13 + 0 -2 + 22k = 13 Add '2' to each side of the equation. -2 + 2 + 22k = 13 + 2 Combine like terms: -2 + 2 = 0 0 + 22k = 13 + 2 22k = 13 + 2 Combine like terms: 13 + 2 = 15 22k = 15 Divide each side by '22'. k = 0.6818181818 Simplifying k = 0.6818181818
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