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Simplifying 71 + [-5k + (-2 + 3)] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Combine like terms: -2 + 3 = 1 71 + [-5k + (1)] = 25 + -1[-1(3k + 4) + -1(4k + 3)] 71 + [-5k + 1] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Reorder the terms: 71 + [1 + -5k] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Remove brackets around [1 + -5k] 71 + 1 + -5k = 25 + -1[-1(3k + 4) + -1(4k + 3)] Combine like terms: 71 + 1 = 72 72 + -5k = 25 + -1[-1(3k + 4) + -1(4k + 3)] Reorder the terms: 72 + -5k = 25 + -1[-1(4 + 3k) + -1(4k + 3)] 72 + -5k = 25 + -1[(4 * -1 + 3k * -1) + -1(4k + 3)] 72 + -5k = 25 + -1[(-4 + -3k) + -1(4k + 3)] Reorder the terms: 72 + -5k = 25 + -1[-4 + -3k + -1(3 + 4k)] 72 + -5k = 25 + -1[-4 + -3k + (3 * -1 + 4k * -1)] 72 + -5k = 25 + -1[-4 + -3k + (-3 + -4k)] Reorder the terms: 72 + -5k = 25 + -1[-4 + -3 + -3k + -4k] Combine like terms: -4 + -3 = -7 72 + -5k = 25 + -1[-7 + -3k + -4k] Combine like terms: -3k + -4k = -7k 72 + -5k = 25 + -1[-7 + -7k] 72 + -5k = 25 + [-7 * -1 + -7k * -1] 72 + -5k = 25 + [7 + 7k] Combine like terms: 25 + 7 = 32 72 + -5k = 32 + 7k Solving 72 + -5k = 32 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. 72 + -5k + -7k = 32 + 7k + -7k Combine like terms: -5k + -7k = -12k 72 + -12k = 32 + 7k + -7k Combine like terms: 7k + -7k = 0 72 + -12k = 32 + 0 72 + -12k = 32 Add '-72' to each side of the equation. 72 + -72 + -12k = 32 + -72 Combine like terms: 72 + -72 = 0 0 + -12k = 32 + -72 -12k = 32 + -72 Combine like terms: 32 + -72 = -40 -12k = -40 Divide each side by '-12'. k = 3.333333333 Simplifying k = 3.333333333
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