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Simplifying 5(4k + -7) = 1 + 8k Reorder the terms: 5(-7 + 4k) = 1 + 8k (-7 * 5 + 4k * 5) = 1 + 8k (-35 + 20k) = 1 + 8k Solving -35 + 20k = 1 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. -35 + 20k + -8k = 1 + 8k + -8k Combine like terms: 20k + -8k = 12k -35 + 12k = 1 + 8k + -8k Combine like terms: 8k + -8k = 0 -35 + 12k = 1 + 0 -35 + 12k = 1 Add '35' to each side of the equation. -35 + 35 + 12k = 1 + 35 Combine like terms: -35 + 35 = 0 0 + 12k = 1 + 35 12k = 1 + 35 Combine like terms: 1 + 35 = 36 12k = 36 Divide each side by '12'. k = 3 Simplifying k = 3
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