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Simplifying 1 + 5(-7k + 8) = -1k + 7 Reorder the terms: 1 + 5(8 + -7k) = -1k + 7 1 + (8 * 5 + -7k * 5) = -1k + 7 1 + (40 + -35k) = -1k + 7 Combine like terms: 1 + 40 = 41 41 + -35k = -1k + 7 Reorder the terms: 41 + -35k = 7 + -1k Solving 41 + -35k = 7 + -1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. 41 + -35k + k = 7 + -1k + k Combine like terms: -35k + k = -34k 41 + -34k = 7 + -1k + k Combine like terms: -1k + k = 0 41 + -34k = 7 + 0 41 + -34k = 7 Add '-41' to each side of the equation. 41 + -41 + -34k = 7 + -41 Combine like terms: 41 + -41 = 0 0 + -34k = 7 + -41 -34k = 7 + -41 Combine like terms: 7 + -41 = -34 -34k = -34 Divide each side by '-34'. k = 1 Simplifying k = 1
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