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Simplifying 5(2 + -4k) + -3(k + -8) = 3k + 8k (2 * 5 + -4k * 5) + -3(k + -8) = 3k + 8k (10 + -20k) + -3(k + -8) = 3k + 8k Reorder the terms: 10 + -20k + -3(-8 + k) = 3k + 8k 10 + -20k + (-8 * -3 + k * -3) = 3k + 8k 10 + -20k + (24 + -3k) = 3k + 8k Reorder the terms: 10 + 24 + -20k + -3k = 3k + 8k Combine like terms: 10 + 24 = 34 34 + -20k + -3k = 3k + 8k Combine like terms: -20k + -3k = -23k 34 + -23k = 3k + 8k Combine like terms: 3k + 8k = 11k 34 + -23k = 11k Solving 34 + -23k = 11k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11k' to each side of the equation. 34 + -23k + -11k = 11k + -11k Combine like terms: -23k + -11k = -34k 34 + -34k = 11k + -11k Combine like terms: 11k + -11k = 0 34 + -34k = 0 Add '-34' to each side of the equation. 34 + -34 + -34k = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -34k = 0 + -34 -34k = 0 + -34 Combine like terms: 0 + -34 = -34 -34k = -34 Divide each side by '-34'. k = 1 Simplifying k = 1
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