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Simplifying 6k + 5(k + 1) + -10k = -8 + -2(k + 12) Reorder the terms: 6k + 5(1 + k) + -10k = -8 + -2(k + 12) 6k + (1 * 5 + k * 5) + -10k = -8 + -2(k + 12) 6k + (5 + 5k) + -10k = -8 + -2(k + 12) Reorder the terms: 5 + 6k + 5k + -10k = -8 + -2(k + 12) Combine like terms: 6k + 5k = 11k 5 + 11k + -10k = -8 + -2(k + 12) Combine like terms: 11k + -10k = 1k 5 + 1k = -8 + -2(k + 12) Reorder the terms: 5 + 1k = -8 + -2(12 + k) 5 + 1k = -8 + (12 * -2 + k * -2) 5 + 1k = -8 + (-24 + -2k) Combine like terms: -8 + -24 = -32 5 + 1k = -32 + -2k Solving 5 + 1k = -32 + -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. 5 + 1k + 2k = -32 + -2k + 2k Combine like terms: 1k + 2k = 3k 5 + 3k = -32 + -2k + 2k Combine like terms: -2k + 2k = 0 5 + 3k = -32 + 0 5 + 3k = -32 Add '-5' to each side of the equation. 5 + -5 + 3k = -32 + -5 Combine like terms: 5 + -5 = 0 0 + 3k = -32 + -5 3k = -32 + -5 Combine like terms: -32 + -5 = -37 3k = -37 Divide each side by '3'. k = -12.33333333 Simplifying k = -12.33333333
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