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Simplifying 2[k + -1(2k + 8) + 3] = 2(k + 5) Reorder the terms: 2[k + -1(8 + 2k) + 3] = 2(k + 5) 2[k + (8 * -1 + 2k * -1) + 3] = 2(k + 5) 2[k + (-8 + -2k) + 3] = 2(k + 5) Reorder the terms: 2[-8 + 3 + k + -2k] = 2(k + 5) Combine like terms: -8 + 3 = -5 2[-5 + k + -2k] = 2(k + 5) Combine like terms: k + -2k = -1k 2[-5 + -1k] = 2(k + 5) [-5 * 2 + -1k * 2] = 2(k + 5) [-10 + -2k] = 2(k + 5) Reorder the terms: -10 + -2k = 2(5 + k) -10 + -2k = (5 * 2 + k * 2) -10 + -2k = (10 + 2k) Solving -10 + -2k = 10 + 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. -10 + -2k + -2k = 10 + 2k + -2k Combine like terms: -2k + -2k = -4k -10 + -4k = 10 + 2k + -2k Combine like terms: 2k + -2k = 0 -10 + -4k = 10 + 0 -10 + -4k = 10 Add '10' to each side of the equation. -10 + 10 + -4k = 10 + 10 Combine like terms: -10 + 10 = 0 0 + -4k = 10 + 10 -4k = 10 + 10 Combine like terms: 10 + 10 = 20 -4k = 20 Divide each side by '-4'. k = -5 Simplifying k = -5
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