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Simplifying -130 = 3(1 + 4k) + 7k -130 = (1 * 3 + 4k * 3) + 7k -130 = (3 + 12k) + 7k Combine like terms: 12k + 7k = 19k -130 = 3 + 19k Solving -130 = 3 + 19k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-19k' to each side of the equation. -130 + -19k = 3 + 19k + -19k Combine like terms: 19k + -19k = 0 -130 + -19k = 3 + 0 -130 + -19k = 3 Add '130' to each side of the equation. -130 + 130 + -19k = 3 + 130 Combine like terms: -130 + 130 = 0 0 + -19k = 3 + 130 -19k = 3 + 130 Combine like terms: 3 + 130 = 133 -19k = 133 Divide each side by '-19'. k = -7 Simplifying k = -7
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