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Simplifying -6[k + -1(2k + 8) + 6] = 2(k + 2) Reorder the terms: -6[k + -1(8 + 2k) + 6] = 2(k + 2) -6[k + (8 * -1 + 2k * -1) + 6] = 2(k + 2) -6[k + (-8 + -2k) + 6] = 2(k + 2) Reorder the terms: -6[-8 + 6 + k + -2k] = 2(k + 2) Combine like terms: -8 + 6 = -2 -6[-2 + k + -2k] = 2(k + 2) Combine like terms: k + -2k = -1k -6[-2 + -1k] = 2(k + 2) [-2 * -6 + -1k * -6] = 2(k + 2) [12 + 6k] = 2(k + 2) Reorder the terms: 12 + 6k = 2(2 + k) 12 + 6k = (2 * 2 + k * 2) 12 + 6k = (4 + 2k) Solving 12 + 6k = 4 + 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 = 4 + 2k + -2k Combine like terms: 6k + -2k = 4k 12 + 4k = 4 + 2k + -2k Combine like terms: 2k + -2k = 0 12 + 4k = 4 + 0 12 + 4k = 4 Add '-12' to each side of the equation. 12 + -12 + 4k = 4 + -12 Combine like terms: 12 + -12 = 0 0 + 4k = 4 + -12 4k = 4 + -12 Combine like terms: 4 + -12 = -8 4k = -8 Divide each side by '4'. k = -2 Simplifying k = -2
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