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Simplifying -5(k + 6) + -5(1 + -5k) = 2k + -3 + 7k + 1 Reorder the terms: -5(6 + k) + -5(1 + -5k) = 2k + -3 + 7k + 1 (6 * -5 + k * -5) + -5(1 + -5k) = 2k + -3 + 7k + 1 (-30 + -5k) + -5(1 + -5k) = 2k + -3 + 7k + 1 -30 + -5k + (1 * -5 + -5k * -5) = 2k + -3 + 7k + 1 -30 + -5k + (-5 + 25k) = 2k + -3 + 7k + 1 Reorder the terms: -30 + -5 + -5k + 25k = 2k + -3 + 7k + 1 Combine like terms: -30 + -5 = -35 -35 + -5k + 25k = 2k + -3 + 7k + 1 Combine like terms: -5k + 25k = 20k -35 + 20k = 2k + -3 + 7k + 1 Reorder the terms: -35 + 20k = -3 + 1 + 2k + 7k Combine like terms: -3 + 1 = -2 -35 + 20k = -2 + 2k + 7k Combine like terms: 2k + 7k = 9k -35 + 20k = -2 + 9k Solving -35 + 20k = -2 + 9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9k' to each side of the equation. -35 + 20k + -9k = -2 + 9k + -9k Combine like terms: 20k + -9k = 11k -35 + 11k = -2 + 9k + -9k Combine like terms: 9k + -9k = 0 -35 + 11k = -2 + 0 -35 + 11k = -2 Add '35' to each side of the equation. -35 + 35 + 11k = -2 + 35 Combine like terms: -35 + 35 = 0 0 + 11k = -2 + 35 11k = -2 + 35 Combine like terms: -2 + 35 = 33 11k = 33 Divide each side by '11'. k = 3 Simplifying k = 3
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