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Simplifying 7k + 31 = 5(1 + -5k) Reorder the terms: 31 + 7k = 5(1 + -5k) 31 + 7k = (1 * 5 + -5k * 5) 31 + 7k = (5 + -25k) Solving 31 + 7k = 5 + -25k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '25k' to each side of the equation. 31 + 7k + 25k = 5 + -25k + 25k Combine like terms: 7k + 25k = 32k 31 + 32k = 5 + -25k + 25k Combine like terms: -25k + 25k = 0 31 + 32k = 5 + 0 31 + 32k = 5 Add '-31' to each side of the equation. 31 + -31 + 32k = 5 + -31 Combine like terms: 31 + -31 = 0 0 + 32k = 5 + -31 32k = 5 + -31 Combine like terms: 5 + -31 = -26 32k = -26 Divide each side by '32'. k = -0.8125 Simplifying k = -0.8125
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