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