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