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Simplifying -4(1 + 3k) = 31 + -7k (1 * -4 + 3k * -4) = 31 + -7k (-4 + -12k) = 31 + -7k Solving -4 + -12k = 31 + -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. -4 + -12k + 7k = 31 + -7k + 7k Combine like terms: -12k + 7k = -5k -4 + -5k = 31 + -7k + 7k Combine like terms: -7k + 7k = 0 -4 + -5k = 31 + 0 -4 + -5k = 31 Add '4' to each side of the equation. -4 + 4 + -5k = 31 + 4 Combine like terms: -4 + 4 = 0 0 + -5k = 31 + 4 -5k = 31 + 4 Combine like terms: 31 + 4 = 35 -5k = 35 Divide each side by '-5'. k = -7 Simplifying k = -7
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