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Simplifying 2[k + -1(4k + 13) + 9] = 2(k + 4) Reorder the terms: 2[k + -1(13 + 4k) + 9] = 2(k + 4) 2[k + (13 * -1 + 4k * -1) + 9] = 2(k + 4) 2[k + (-13 + -4k) + 9] = 2(k + 4) Reorder the terms: 2[-13 + 9 + k + -4k] = 2(k + 4) Combine like terms: -13 + 9 = -4 2[-4 + k + -4k] = 2(k + 4) Combine like terms: k + -4k = -3k 2[-4 + -3k] = 2(k + 4) [-4 * 2 + -3k * 2] = 2(k + 4) [-8 + -6k] = 2(k + 4) Reorder the terms: -8 + -6k = 2(4 + k) -8 + -6k = (4 * 2 + k * 2) -8 + -6k = (8 + 2k) Solving -8 + -6k = 8 + 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. -8 + -6k + -2k = 8 + 2k + -2k Combine like terms: -6k + -2k = -8k -8 + -8k = 8 + 2k + -2k Combine like terms: 2k + -2k = 0 -8 + -8k = 8 + 0 -8 + -8k = 8 Add '8' to each side of the equation. -8 + 8 + -8k = 8 + 8 Combine like terms: -8 + 8 = 0 0 + -8k = 8 + 8 -8k = 8 + 8 Combine like terms: 8 + 8 = 16 -8k = 16 Divide each side by '-8'. k = -2 Simplifying k = -2
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