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Simplifying 3 + 8k + k + 1 = -8(k + 3) + -3(-4k + -6) Reorder the terms: 3 + 1 + 8k + k = -8(k + 3) + -3(-4k + -6) Combine like terms: 3 + 1 = 4 4 + 8k + k = -8(k + 3) + -3(-4k + -6) Combine like terms: 8k + k = 9k 4 + 9k = -8(k + 3) + -3(-4k + -6) Reorder the terms: 4 + 9k = -8(3 + k) + -3(-4k + -6) 4 + 9k = (3 * -8 + k * -8) + -3(-4k + -6) 4 + 9k = (-24 + -8k) + -3(-4k + -6) Reorder the terms: 4 + 9k = -24 + -8k + -3(-6 + -4k) 4 + 9k = -24 + -8k + (-6 * -3 + -4k * -3) 4 + 9k = -24 + -8k + (18 + 12k) Reorder the terms: 4 + 9k = -24 + 18 + -8k + 12k Combine like terms: -24 + 18 = -6 4 + 9k = -6 + -8k + 12k Combine like terms: -8k + 12k = 4k 4 + 9k = -6 + 4k Solving 4 + 9k = -6 + 4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4k' to each side of the equation. 4 + 9k + -4k = -6 + 4k + -4k Combine like terms: 9k + -4k = 5k 4 + 5k = -6 + 4k + -4k Combine like terms: 4k + -4k = 0 4 + 5k = -6 + 0 4 + 5k = -6 Add '-4' to each side of the equation. 4 + -4 + 5k = -6 + -4 Combine like terms: 4 + -4 = 0 0 + 5k = -6 + -4 5k = -6 + -4 Combine like terms: -6 + -4 = -10 5k = -10 Divide each side by '5'. k = -2 Simplifying k = -2
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