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Simplifying 4(4k + 1) + -8(k + -1) = 3(2k + 3) + -1 Reorder the terms: 4(1 + 4k) + -8(k + -1) = 3(2k + 3) + -1 (1 * 4 + 4k * 4) + -8(k + -1) = 3(2k + 3) + -1 (4 + 16k) + -8(k + -1) = 3(2k + 3) + -1 Reorder the terms: 4 + 16k + -8(-1 + k) = 3(2k + 3) + -1 4 + 16k + (-1 * -8 + k * -8) = 3(2k + 3) + -1 4 + 16k + (8 + -8k) = 3(2k + 3) + -1 Reorder the terms: 4 + 8 + 16k + -8k = 3(2k + 3) + -1 Combine like terms: 4 + 8 = 12 12 + 16k + -8k = 3(2k + 3) + -1 Combine like terms: 16k + -8k = 8k 12 + 8k = 3(2k + 3) + -1 Reorder the terms: 12 + 8k = 3(3 + 2k) + -1 12 + 8k = (3 * 3 + 2k * 3) + -1 12 + 8k = (9 + 6k) + -1 Reorder the terms: 12 + 8k = 9 + -1 + 6k Combine like terms: 9 + -1 = 8 12 + 8k = 8 + 6k Solving 12 + 8k = 8 + 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. 12 + 8k + -6k = 8 + 6k + -6k Combine like terms: 8k + -6k = 2k 12 + 2k = 8 + 6k + -6k Combine like terms: 6k + -6k = 0 12 + 2k = 8 + 0 12 + 2k = 8 Add '-12' to each side of the equation. 12 + -12 + 2k = 8 + -12 Combine like terms: 12 + -12 = 0 0 + 2k = 8 + -12 2k = 8 + -12 Combine like terms: 8 + -12 = -4 2k = -4 Divide each side by '2'. k = -2 Simplifying k = -2
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