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Simplifying 2[k + -1(4k + 13) + 5] = 2(k + 8) Reorder the terms: 2[k + -1(13 + 4k) + 5] = 2(k + 8) 2[k + (13 * -1 + 4k * -1) + 5] = 2(k + 8) 2[k + (-13 + -4k) + 5] = 2(k + 8) Reorder the terms: 2[-13 + 5 + k + -4k] = 2(k + 8) Combine like terms: -13 + 5 = -8 2[-8 + k + -4k] = 2(k + 8) Combine like terms: k + -4k = -3k 2[-8 + -3k] = 2(k + 8) [-8 * 2 + -3k * 2] = 2(k + 8) [-16 + -6k] = 2(k + 8) Reorder the terms: -16 + -6k = 2(8 + k) -16 + -6k = (8 * 2 + k * 2) -16 + -6k = (16 + 2k) Solving -16 + -6k = 16 + 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. -16 + -6k + -2k = 16 + 2k + -2k Combine like terms: -6k + -2k = -8k -16 + -8k = 16 + 2k + -2k Combine like terms: 2k + -2k = 0 -16 + -8k = 16 + 0 -16 + -8k = 16 Add '16' to each side of the equation. -16 + 16 + -8k = 16 + 16 Combine like terms: -16 + 16 = 0 0 + -8k = 16 + 16 -8k = 16 + 16 Combine like terms: 16 + 16 = 32 -8k = 32 Divide each side by '-8'. k = -4 Simplifying k = -4
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