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Simplifying 3(4 + -5k) + -5(7 + -2k) + 6 = 3k + 7 (4 * 3 + -5k * 3) + -5(7 + -2k) + 6 = 3k + 7 (12 + -15k) + -5(7 + -2k) + 6 = 3k + 7 12 + -15k + (7 * -5 + -2k * -5) + 6 = 3k + 7 12 + -15k + (-35 + 10k) + 6 = 3k + 7 Reorder the terms: 12 + -35 + 6 + -15k + 10k = 3k + 7 Combine like terms: 12 + -35 = -23 -23 + 6 + -15k + 10k = 3k + 7 Combine like terms: -23 + 6 = -17 -17 + -15k + 10k = 3k + 7 Combine like terms: -15k + 10k = -5k -17 + -5k = 3k + 7 Reorder the terms: -17 + -5k = 7 + 3k Solving -17 + -5k = 7 + 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. -17 + -5k + -3k = 7 + 3k + -3k Combine like terms: -5k + -3k = -8k -17 + -8k = 7 + 3k + -3k Combine like terms: 3k + -3k = 0 -17 + -8k = 7 + 0 -17 + -8k = 7 Add '17' to each side of the equation. -17 + 17 + -8k = 7 + 17 Combine like terms: -17 + 17 = 0 0 + -8k = 7 + 17 -8k = 7 + 17 Combine like terms: 7 + 17 = 24 -8k = 24 Divide each side by '-8'. k = -3 Simplifying k = -3
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