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Simplifying -2[4(k + 2) + -3(k + 1)] = 14 + 2k Reorder the terms: -2[4(2 + k) + -3(k + 1)] = 14 + 2k -2[(2 * 4 + k * 4) + -3(k + 1)] = 14 + 2k -2[(8 + 4k) + -3(k + 1)] = 14 + 2k Reorder the terms: -2[8 + 4k + -3(1 + k)] = 14 + 2k -2[8 + 4k + (1 * -3 + k * -3)] = 14 + 2k -2[8 + 4k + (-3 + -3k)] = 14 + 2k Reorder the terms: -2[8 + -3 + 4k + -3k] = 14 + 2k Combine like terms: 8 + -3 = 5 -2[5 + 4k + -3k] = 14 + 2k Combine like terms: 4k + -3k = 1k -2[5 + 1k] = 14 + 2k [5 * -2 + 1k * -2] = 14 + 2k [-10 + -2k] = 14 + 2k Solving -10 + -2k = 14 + 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 = 14 + 2k + -2k Combine like terms: -2k + -2k = -4k -10 + -4k = 14 + 2k + -2k Combine like terms: 2k + -2k = 0 -10 + -4k = 14 + 0 -10 + -4k = 14 Add '10' to each side of the equation. -10 + 10 + -4k = 14 + 10 Combine like terms: -10 + 10 = 0 0 + -4k = 14 + 10 -4k = 14 + 10 Combine like terms: 14 + 10 = 24 -4k = 24 Divide each side by '-4'. k = -6 Simplifying k = -6
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