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Simplifying 4(4k + 2) + -8(k + -1) = 3(2k + 1) + -2 Reorder the terms: 4(2 + 4k) + -8(k + -1) = 3(2k + 1) + -2 (2 * 4 + 4k * 4) + -8(k + -1) = 3(2k + 1) + -2 (8 + 16k) + -8(k + -1) = 3(2k + 1) + -2 Reorder the terms: 8 + 16k + -8(-1 + k) = 3(2k + 1) + -2 8 + 16k + (-1 * -8 + k * -8) = 3(2k + 1) + -2 8 + 16k + (8 + -8k) = 3(2k + 1) + -2 Reorder the terms: 8 + 8 + 16k + -8k = 3(2k + 1) + -2 Combine like terms: 8 + 8 = 16 16 + 16k + -8k = 3(2k + 1) + -2 Combine like terms: 16k + -8k = 8k 16 + 8k = 3(2k + 1) + -2 Reorder the terms: 16 + 8k = 3(1 + 2k) + -2 16 + 8k = (1 * 3 + 2k * 3) + -2 16 + 8k = (3 + 6k) + -2 Reorder the terms: 16 + 8k = 3 + -2 + 6k Combine like terms: 3 + -2 = 1 16 + 8k = 1 + 6k Solving 16 + 8k = 1 + 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. 16 + 8k + -6k = 1 + 6k + -6k Combine like terms: 8k + -6k = 2k 16 + 2k = 1 + 6k + -6k Combine like terms: 6k + -6k = 0 16 + 2k = 1 + 0 16 + 2k = 1 Add '-16' to each side of the equation. 16 + -16 + 2k = 1 + -16 Combine like terms: 16 + -16 = 0 0 + 2k = 1 + -16 2k = 1 + -16 Combine like terms: 1 + -16 = -15 2k = -15 Divide each side by '2'. k = -7.5 Simplifying k = -7.5
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