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Simplifying 4(4k + 1) + -8(k + -1) = 0 Reorder the terms: 4(1 + 4k) + -8(k + -1) = 0 (1 * 4 + 4k * 4) + -8(k + -1) = 0 (4 + 16k) + -8(k + -1) = 0 Reorder the terms: 4 + 16k + -8(-1 + k) = 0 4 + 16k + (-1 * -8 + k * -8) = 0 4 + 16k + (8 + -8k) = 0 Reorder the terms: 4 + 8 + 16k + -8k = 0 Combine like terms: 4 + 8 = 12 12 + 16k + -8k = 0 Combine like terms: 16k + -8k = 8k 12 + 8k = 0 Solving 12 + 8k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 8k = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 8k = 0 + -12 8k = 0 + -12 Combine like terms: 0 + -12 = -12 8k = -12 Divide each side by '8'. k = -1.5 Simplifying k = -1.5
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