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Simplifying 4(4k + 1) + -8(k + -2) = 3(2k + 1) + -1 Reorder the terms: 4(1 + 4k) + -8(k + -2) = 3(2k + 1) + -1 (1 * 4 + 4k * 4) + -8(k + -2) = 3(2k + 1) + -1 (4 + 16k) + -8(k + -2) = 3(2k + 1) + -1 Reorder the terms: 4 + 16k + -8(-2 + k) = 3(2k + 1) + -1 4 + 16k + (-2 * -8 + k * -8) = 3(2k + 1) + -1 4 + 16k + (16 + -8k) = 3(2k + 1) + -1 Reorder the terms: 4 + 16 + 16k + -8k = 3(2k + 1) + -1 Combine like terms: 4 + 16 = 20 20 + 16k + -8k = 3(2k + 1) + -1 Combine like terms: 16k + -8k = 8k 20 + 8k = 3(2k + 1) + -1 Reorder the terms: 20 + 8k = 3(1 + 2k) + -1 20 + 8k = (1 * 3 + 2k * 3) + -1 20 + 8k = (3 + 6k) + -1 Reorder the terms: 20 + 8k = 3 + -1 + 6k Combine like terms: 3 + -1 = 2 20 + 8k = 2 + 6k Solving 20 + 8k = 2 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 20 + 8k + -6k = 2 + 6k + -6k Combine like terms: 8k + -6k = 2k 20 + 2k = 2 + 6k + -6k Combine like terms: 6k + -6k = 0 20 + 2k = 2 + 0 20 + 2k = 2 Add '-20' to each side of the equation. 20 + -20 + 2k = 2 + -20 Combine like terms: 20 + -20 = 0 0 + 2k = 2 + -20 2k = 2 + -20 Combine like terms: 2 + -20 = -18 2k = -18 Divide each side by '2'. k = -9 Simplifying k = -9
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