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Simplifying -5(k + 6) + -5(1 + -5k) = k + -3 + 7k + 1 Reorder the terms: -5(6 + k) + -5(1 + -5k) = k + -3 + 7k + 1 (6 * -5 + k * -5) + -5(1 + -5k) = k + -3 + 7k + 1 (-30 + -5k) + -5(1 + -5k) = k + -3 + 7k + 1 -30 + -5k + (1 * -5 + -5k * -5) = k + -3 + 7k + 1 -30 + -5k + (-5 + 25k) = k + -3 + 7k + 1 Reorder the terms: -30 + -5 + -5k + 25k = k + -3 + 7k + 1 Combine like terms: -30 + -5 = -35 -35 + -5k + 25k = k + -3 + 7k + 1 Combine like terms: -5k + 25k = 20k -35 + 20k = k + -3 + 7k + 1 Reorder the terms: -35 + 20k = -3 + 1 + k + 7k Combine like terms: -3 + 1 = -2 -35 + 20k = -2 + k + 7k Combine like terms: k + 7k = 8k -35 + 20k = -2 + 8k Solving -35 + 20k = -2 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. -35 + 20k + -8k = -2 + 8k + -8k Combine like terms: 20k + -8k = 12k -35 + 12k = -2 + 8k + -8k Combine like terms: 8k + -8k = 0 -35 + 12k = -2 + 0 -35 + 12k = -2 Add '35' to each side of the equation. -35 + 35 + 12k = -2 + 35 Combine like terms: -35 + 35 = 0 0 + 12k = -2 + 35 12k = -2 + 35 Combine like terms: -2 + 35 = 33 12k = 33 Divide each side by '12'. k = 2.75 Simplifying k = 2.75
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