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Simplifying 3 + 3k + -2 + -5k = 4(5 + -2k) + -1(-3k + -8) Reorder the terms: 3 + -2 + 3k + -5k = 4(5 + -2k) + -1(-3k + -8) Combine like terms: 3 + -2 = 1 1 + 3k + -5k = 4(5 + -2k) + -1(-3k + -8) Combine like terms: 3k + -5k = -2k 1 + -2k = 4(5 + -2k) + -1(-3k + -8) 1 + -2k = (5 * 4 + -2k * 4) + -1(-3k + -8) 1 + -2k = (20 + -8k) + -1(-3k + -8) Reorder the terms: 1 + -2k = 20 + -8k + -1(-8 + -3k) 1 + -2k = 20 + -8k + (-8 * -1 + -3k * -1) 1 + -2k = 20 + -8k + (8 + 3k) Reorder the terms: 1 + -2k = 20 + 8 + -8k + 3k Combine like terms: 20 + 8 = 28 1 + -2k = 28 + -8k + 3k Combine like terms: -8k + 3k = -5k 1 + -2k = 28 + -5k Solving 1 + -2k = 28 + -5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5k' to each side of the equation. 1 + -2k + 5k = 28 + -5k + 5k Combine like terms: -2k + 5k = 3k 1 + 3k = 28 + -5k + 5k Combine like terms: -5k + 5k = 0 1 + 3k = 28 + 0 1 + 3k = 28 Add '-1' to each side of the equation. 1 + -1 + 3k = 28 + -1 Combine like terms: 1 + -1 = 0 0 + 3k = 28 + -1 3k = 28 + -1 Combine like terms: 28 + -1 = 27 3k = 27 Divide each side by '3'. k = 9 Simplifying k = 9
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