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Simplifying 8(1 + 4k) + -1k = -40 + 7k (1 * 8 + 4k * 8) + -1k = -40 + 7k (8 + 32k) + -1k = -40 + 7k Combine like terms: 32k + -1k = 31k 8 + 31k = -40 + 7k Solving 8 + 31k = -40 + 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. 8 + 31k + -7k = -40 + 7k + -7k Combine like terms: 31k + -7k = 24k 8 + 24k = -40 + 7k + -7k Combine like terms: 7k + -7k = 0 8 + 24k = -40 + 0 8 + 24k = -40 Add '-8' to each side of the equation. 8 + -8 + 24k = -40 + -8 Combine like terms: 8 + -8 = 0 0 + 24k = -40 + -8 24k = -40 + -8 Combine like terms: -40 + -8 = -48 24k = -48 Divide each side by '24'. k = -2 Simplifying k = -2
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