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Simplifying 5 + -3[5 + -3(4k + 3)] = 5k + -3[5k + -3(5k + 3)] Reorder the terms: 5 + -3[5 + -3(3 + 4k)] = 5k + -3[5k + -3(5k + 3)] 5 + -3[5 + (3 * -3 + 4k * -3)] = 5k + -3[5k + -3(5k + 3)] 5 + -3[5 + (-9 + -12k)] = 5k + -3[5k + -3(5k + 3)] Combine like terms: 5 + -9 = -4 5 + -3[-4 + -12k] = 5k + -3[5k + -3(5k + 3)] 5 + [-4 * -3 + -12k * -3] = 5k + -3[5k + -3(5k + 3)] 5 + [12 + 36k] = 5k + -3[5k + -3(5k + 3)] Combine like terms: 5 + 12 = 17 17 + 36k = 5k + -3[5k + -3(5k + 3)] Reorder the terms: 17 + 36k = 5k + -3[5k + -3(3 + 5k)] 17 + 36k = 5k + -3[5k + (3 * -3 + 5k * -3)] 17 + 36k = 5k + -3[5k + (-9 + -15k)] Reorder the terms: 17 + 36k = 5k + -3[-9 + 5k + -15k] Combine like terms: 5k + -15k = -10k 17 + 36k = 5k + -3[-9 + -10k] 17 + 36k = 5k + [-9 * -3 + -10k * -3] 17 + 36k = 5k + [27 + 30k] Reorder the terms: 17 + 36k = 27 + 5k + 30k Combine like terms: 5k + 30k = 35k 17 + 36k = 27 + 35k Solving 17 + 36k = 27 + 35k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-35k' to each side of the equation. 17 + 36k + -35k = 27 + 35k + -35k Combine like terms: 36k + -35k = 1k 17 + 1k = 27 + 35k + -35k Combine like terms: 35k + -35k = 0 17 + 1k = 27 + 0 17 + 1k = 27 Add '-17' to each side of the equation. 17 + -17 + 1k = 27 + -17 Combine like terms: 17 + -17 = 0 0 + 1k = 27 + -17 1k = 27 + -17 Combine like terms: 27 + -17 = 10 1k = 10 Divide each side by '1'. k = 10 Simplifying k = 10
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