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Simplifying 2[k + -1(2k + 12) + 10] = 2(k + 2) Reorder the terms: 2[k + -1(12 + 2k) + 10] = 2(k + 2) 2[k + (12 * -1 + 2k * -1) + 10] = 2(k + 2) 2[k + (-12 + -2k) + 10] = 2(k + 2) Reorder the terms: 2[-12 + 10 + k + -2k] = 2(k + 2) Combine like terms: -12 + 10 = -2 2[-2 + k + -2k] = 2(k + 2) Combine like terms: k + -2k = -1k 2[-2 + -1k] = 2(k + 2) [-2 * 2 + -1k * 2] = 2(k + 2) [-4 + -2k] = 2(k + 2) Reorder the terms: -4 + -2k = 2(2 + k) -4 + -2k = (2 * 2 + k * 2) -4 + -2k = (4 + 2k) Solving -4 + -2k = 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. -4 + -2k + -2k = 4 + 2k + -2k Combine like terms: -2k + -2k = -4k -4 + -4k = 4 + 2k + -2k Combine like terms: 2k + -2k = 0 -4 + -4k = 4 + 0 -4 + -4k = 4 Add '4' to each side of the equation. -4 + 4 + -4k = 4 + 4 Combine like terms: -4 + 4 = 0 0 + -4k = 4 + 4 -4k = 4 + 4 Combine like terms: 4 + 4 = 8 -4k = 8 Divide each side by '-4'. k = -2 Simplifying k = -2
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