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Simplifying 8(k + 5) + -1(7 + -3k) = 10k Reorder the terms: 8(5 + k) + -1(7 + -3k) = 10k (5 * 8 + k * 8) + -1(7 + -3k) = 10k (40 + 8k) + -1(7 + -3k) = 10k 40 + 8k + (7 * -1 + -3k * -1) = 10k 40 + 8k + (-7 + 3k) = 10k Reorder the terms: 40 + -7 + 8k + 3k = 10k Combine like terms: 40 + -7 = 33 33 + 8k + 3k = 10k Combine like terms: 8k + 3k = 11k 33 + 11k = 10k Solving 33 + 11k = 10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10k' to each side of the equation. 33 + 11k + -10k = 10k + -10k Combine like terms: 11k + -10k = 1k 33 + 1k = 10k + -10k Combine like terms: 10k + -10k = 0 33 + 1k = 0 Add '-33' to each side of the equation. 33 + -33 + 1k = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 1k = 0 + -33 1k = 0 + -33 Combine like terms: 0 + -33 = -33 1k = -33 Divide each side by '1'. k = -33 Simplifying k = -33
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