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