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