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Simplifying -40 = -5(1 + -7k) + 8(k + 1) -40 = (1 * -5 + -7k * -5) + 8(k + 1) -40 = (-5 + 35k) + 8(k + 1) Reorder the terms: -40 = -5 + 35k + 8(1 + k) -40 = -5 + 35k + (1 * 8 + k * 8) -40 = -5 + 35k + (8 + 8k) Reorder the terms: -40 = -5 + 8 + 35k + 8k Combine like terms: -5 + 8 = 3 -40 = 3 + 35k + 8k Combine like terms: 35k + 8k = 43k -40 = 3 + 43k Solving -40 = 3 + 43k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-43k' to each side of the equation. -40 + -43k = 3 + 43k + -43k Combine like terms: 43k + -43k = 0 -40 + -43k = 3 + 0 -40 + -43k = 3 Add '40' to each side of the equation. -40 + 40 + -43k = 3 + 40 Combine like terms: -40 + 40 = 0 0 + -43k = 3 + 40 -43k = 3 + 40 Combine like terms: 3 + 40 = 43 -43k = 43 Divide each side by '-43'. k = -1 Simplifying k = -1
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