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Simplifying 4(4k + 2) + -8(k + -1) = 3(2k + 5) + -1 Reorder the terms: 4(2 + 4k) + -8(k + -1) = 3(2k + 5) + -1 (2 * 4 + 4k * 4) + -8(k + -1) = 3(2k + 5) + -1 (8 + 16k) + -8(k + -1) = 3(2k + 5) + -1 Reorder the terms: 8 + 16k + -8(-1 + k) = 3(2k + 5) + -1 8 + 16k + (-1 * -8 + k * -8) = 3(2k + 5) + -1 8 + 16k + (8 + -8k) = 3(2k + 5) + -1 Reorder the terms: 8 + 8 + 16k + -8k = 3(2k + 5) + -1 Combine like terms: 8 + 8 = 16 16 + 16k + -8k = 3(2k + 5) + -1 Combine like terms: 16k + -8k = 8k 16 + 8k = 3(2k + 5) + -1 Reorder the terms: 16 + 8k = 3(5 + 2k) + -1 16 + 8k = (5 * 3 + 2k * 3) + -1 16 + 8k = (15 + 6k) + -1 Reorder the terms: 16 + 8k = 15 + -1 + 6k Combine like terms: 15 + -1 = 14 16 + 8k = 14 + 6k Solving 16 + 8k = 14 + 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 = 14 + 6k + -6k Combine like terms: 8k + -6k = 2k 16 + 2k = 14 + 6k + -6k Combine like terms: 6k + -6k = 0 16 + 2k = 14 + 0 16 + 2k = 14 Add '-16' to each side of the equation. 16 + -16 + 2k = 14 + -16 Combine like terms: 16 + -16 = 0 0 + 2k = 14 + -16 2k = 14 + -16 Combine like terms: 14 + -16 = -2 2k = -2 Divide each side by '2'. k = -1 Simplifying k = -1
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