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Simplifying 5 + -1(6k + 1) = 2(5k + -3 + -1k + -2) Reorder the terms: 5 + -1(1 + 6k) = 2(5k + -3 + -1k + -2) 5 + (1 * -1 + 6k * -1) = 2(5k + -3 + -1k + -2) 5 + (-1 + -6k) = 2(5k + -3 + -1k + -2) Combine like terms: 5 + -1 = 4 4 + -6k = 2(5k + -3 + -1k + -2) Reorder the terms: 4 + -6k = 2(-3 + -2 + 5k + -1k) Combine like terms: -3 + -2 = -5 4 + -6k = 2(-5 + 5k + -1k) Combine like terms: 5k + -1k = 4k 4 + -6k = 2(-5 + 4k) 4 + -6k = (-5 * 2 + 4k * 2) 4 + -6k = (-10 + 8k) Solving 4 + -6k = -10 + 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. 4 + -6k + -8k = -10 + 8k + -8k Combine like terms: -6k + -8k = -14k 4 + -14k = -10 + 8k + -8k Combine like terms: 8k + -8k = 0 4 + -14k = -10 + 0 4 + -14k = -10 Add '-4' to each side of the equation. 4 + -4 + -14k = -10 + -4 Combine like terms: 4 + -4 = 0 0 + -14k = -10 + -4 -14k = -10 + -4 Combine like terms: -10 + -4 = -14 -14k = -14 Divide each side by '-14'. k = 1 Simplifying k = 1
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