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Simplifying 2[k + -1(4k + 7) + 1] = 2(k + 6) Reorder the terms: 2[k + -1(7 + 4k) + 1] = 2(k + 6) 2[k + (7 * -1 + 4k * -1) + 1] = 2(k + 6) 2[k + (-7 + -4k) + 1] = 2(k + 6) Reorder the terms: 2[-7 + 1 + k + -4k] = 2(k + 6) Combine like terms: -7 + 1 = -6 2[-6 + k + -4k] = 2(k + 6) Combine like terms: k + -4k = -3k 2[-6 + -3k] = 2(k + 6) [-6 * 2 + -3k * 2] = 2(k + 6) [-12 + -6k] = 2(k + 6) Reorder the terms: -12 + -6k = 2(6 + k) -12 + -6k = (6 * 2 + k * 2) -12 + -6k = (12 + 2k) Solving -12 + -6k = 12 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. -12 + -6k + -2k = 12 + 2k + -2k Combine like terms: -6k + -2k = -8k -12 + -8k = 12 + 2k + -2k Combine like terms: 2k + -2k = 0 -12 + -8k = 12 + 0 -12 + -8k = 12 Add '12' to each side of the equation. -12 + 12 + -8k = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -8k = 12 + 12 -8k = 12 + 12 Combine like terms: 12 + 12 = 24 -8k = 24 Divide each side by '-8'. k = -3 Simplifying k = -3
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