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Simplifying 3 + -2(-5 + -6k) = -83 3 + (-5 * -2 + -6k * -2) = -83 3 + (10 + 12k) = -83 Combine like terms: 3 + 10 = 13 13 + 12k = -83 Solving 13 + 12k = -83 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 12k = -83 + -13 Combine like terms: 13 + -13 = 0 0 + 12k = -83 + -13 12k = -83 + -13 Combine like terms: -83 + -13 = -96 12k = -96 Divide each side by '12'. k = -8 Simplifying k = -8
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