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Simplifying -6(1 + -2k) = 7k + 29 (1 * -6 + -2k * -6) = 7k + 29 (-6 + 12k) = 7k + 29 Reorder the terms: -6 + 12k = 29 + 7k Solving -6 + 12k = 29 + 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. -6 + 12k + -7k = 29 + 7k + -7k Combine like terms: 12k + -7k = 5k -6 + 5k = 29 + 7k + -7k Combine like terms: 7k + -7k = 0 -6 + 5k = 29 + 0 -6 + 5k = 29 Add '6' to each side of the equation. -6 + 6 + 5k = 29 + 6 Combine like terms: -6 + 6 = 0 0 + 5k = 29 + 6 5k = 29 + 6 Combine like terms: 29 + 6 = 35 5k = 35 Divide each side by '5'. k = 7 Simplifying k = 7
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