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Simplifying 8(k + 7) + -1(k + -5) = 40 Reorder the terms: 8(7 + k) + -1(k + -5) = 40 (7 * 8 + k * 8) + -1(k + -5) = 40 (56 + 8k) + -1(k + -5) = 40 Reorder the terms: 56 + 8k + -1(-5 + k) = 40 56 + 8k + (-5 * -1 + k * -1) = 40 56 + 8k + (5 + -1k) = 40 Reorder the terms: 56 + 5 + 8k + -1k = 40 Combine like terms: 56 + 5 = 61 61 + 8k + -1k = 40 Combine like terms: 8k + -1k = 7k 61 + 7k = 40 Solving 61 + 7k = 40 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-61' to each side of the equation. 61 + -61 + 7k = 40 + -61 Combine like terms: 61 + -61 = 0 0 + 7k = 40 + -61 7k = 40 + -61 Combine like terms: 40 + -61 = -21 7k = -21 Divide each side by '7'. k = -3 Simplifying k = -3
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