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Simplifying 71 + [-5k + (-2K + 3)] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Reorder the terms: 71 + [-5k + (3 + -2K)] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Remove parenthesis around (3 + -2K) 71 + [-5k + 3 + -2K] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Reorder the terms: 71 + [3 + -2K + -5k] = 25 + -1[-1(3k + 4) + -1(4k + 3)] Remove brackets around [3 + -2K + -5k] 71 + 3 + -2K + -5k = 25 + -1[-1(3k + 4) + -1(4k + 3)] Combine like terms: 71 + 3 = 74 74 + -2K + -5k = 25 + -1[-1(3k + 4) + -1(4k + 3)] Reorder the terms: 74 + -2K + -5k = 25 + -1[-1(4 + 3k) + -1(4k + 3)] 74 + -2K + -5k = 25 + -1[(4 * -1 + 3k * -1) + -1(4k + 3)] 74 + -2K + -5k = 25 + -1[(-4 + -3k) + -1(4k + 3)] Reorder the terms: 74 + -2K + -5k = 25 + -1[-4 + -3k + -1(3 + 4k)] 74 + -2K + -5k = 25 + -1[-4 + -3k + (3 * -1 + 4k * -1)] 74 + -2K + -5k = 25 + -1[-4 + -3k + (-3 + -4k)] Reorder the terms: 74 + -2K + -5k = 25 + -1[-4 + -3 + -3k + -4k] Combine like terms: -4 + -3 = -7 74 + -2K + -5k = 25 + -1[-7 + -3k + -4k] Combine like terms: -3k + -4k = -7k 74 + -2K + -5k = 25 + -1[-7 + -7k] 74 + -2K + -5k = 25 + [-7 * -1 + -7k * -1] 74 + -2K + -5k = 25 + [7 + 7k] Combine like terms: 25 + 7 = 32 74 + -2K + -5k = 32 + 7k Solving 74 + -2K + -5k = 32 + 7k Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-74' to each side of the equation. 74 + -2K + -74 + -5k = 32 + -74 + 7k Reorder the terms: 74 + -74 + -2K + -5k = 32 + -74 + 7k Combine like terms: 74 + -74 = 0 0 + -2K + -5k = 32 + -74 + 7k -2K + -5k = 32 + -74 + 7k Combine like terms: 32 + -74 = -42 -2K + -5k = -42 + 7k Add '5k' to each side of the equation. -2K + -5k + 5k = -42 + 7k + 5k Combine like terms: -5k + 5k = 0 -2K + 0 = -42 + 7k + 5k -2K = -42 + 7k + 5k Combine like terms: 7k + 5k = 12k -2K = -42 + 12k Divide each side by '-2'. K = 21 + -6k Simplifying K = 21 + -6k
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