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Simplifying -1[-1(-1k)] + -1(-2 + k) = -1k + -1(4k + 3) Remove parenthesis around (-1k) -1[-1 * -1k] + -1(-2 + k) = -1k + -1(4k + 3) Multiply -1 * -1 -1[1k] + -1(-2 + k) = -1k + -1(4k + 3) Remove brackets around [1k] -1 * 1k + -1(-2 + k) = -1k + -1(4k + 3) Multiply -1 * 1 -1k + -1(-2 + k) = -1k + -1(4k + 3) -1k + (-2 * -1 + k * -1) = -1k + -1(4k + 3) -1k + (2 + -1k) = -1k + -1(4k + 3) Reorder the terms: 2 + -1k + -1k = -1k + -1(4k + 3) Combine like terms: -1k + -1k = -2k 2 + -2k = -1k + -1(4k + 3) Reorder the terms: 2 + -2k = -1k + -1(3 + 4k) 2 + -2k = -1k + (3 * -1 + 4k * -1) 2 + -2k = -1k + (-3 + -4k) Reorder the terms: 2 + -2k = -3 + -1k + -4k Combine like terms: -1k + -4k = -5k 2 + -2k = -3 + -5k Solving 2 + -2k = -3 + -5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5k' to each side of the equation. 2 + -2k + 5k = -3 + -5k + 5k Combine like terms: -2k + 5k = 3k 2 + 3k = -3 + -5k + 5k Combine like terms: -5k + 5k = 0 2 + 3k = -3 + 0 2 + 3k = -3 Add '-2' to each side of the equation. 2 + -2 + 3k = -3 + -2 Combine like terms: 2 + -2 = 0 0 + 3k = -3 + -2 3k = -3 + -2 Combine like terms: -3 + -2 = -5 3k = -5 Divide each side by '3'. k = -1.666666667 Simplifying k = -1.666666667
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