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Simplifying 5 = 8(4 + -1k) + 3(5k + 5) 5 = (4 * 8 + -1k * 8) + 3(5k + 5) 5 = (32 + -8k) + 3(5k + 5) Reorder the terms: 5 = 32 + -8k + 3(5 + 5k) 5 = 32 + -8k + (5 * 3 + 5k * 3) 5 = 32 + -8k + (15 + 15k) Reorder the terms: 5 = 32 + 15 + -8k + 15k Combine like terms: 32 + 15 = 47 5 = 47 + -8k + 15k Combine like terms: -8k + 15k = 7k 5 = 47 + 7k Solving 5 = 47 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. 5 + -7k = 47 + 7k + -7k Combine like terms: 7k + -7k = 0 5 + -7k = 47 + 0 5 + -7k = 47 Add '-5' to each side of the equation. 5 + -5 + -7k = 47 + -5 Combine like terms: 5 + -5 = 0 0 + -7k = 47 + -5 -7k = 47 + -5 Combine like terms: 47 + -5 = 42 -7k = 42 Divide each side by '-7'. k = -6 Simplifying k = -6
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