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Simplifying 5 + -1(6k + 1) = 2(5k + -3) + -1(k + -2) Reorder the terms: 5 + -1(1 + 6k) = 2(5k + -3) + -1(k + -2) 5 + (1 * -1 + 6k * -1) = 2(5k + -3) + -1(k + -2) 5 + (-1 + -6k) = 2(5k + -3) + -1(k + -2) Combine like terms: 5 + -1 = 4 4 + -6k = 2(5k + -3) + -1(k + -2) Reorder the terms: 4 + -6k = 2(-3 + 5k) + -1(k + -2) 4 + -6k = (-3 * 2 + 5k * 2) + -1(k + -2) 4 + -6k = (-6 + 10k) + -1(k + -2) Reorder the terms: 4 + -6k = -6 + 10k + -1(-2 + k) 4 + -6k = -6 + 10k + (-2 * -1 + k * -1) 4 + -6k = -6 + 10k + (2 + -1k) Reorder the terms: 4 + -6k = -6 + 2 + 10k + -1k Combine like terms: -6 + 2 = -4 4 + -6k = -4 + 10k + -1k Combine like terms: 10k + -1k = 9k 4 + -6k = -4 + 9k Solving 4 + -6k = -4 + 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. 4 + -6k + -9k = -4 + 9k + -9k Combine like terms: -6k + -9k = -15k 4 + -15k = -4 + 9k + -9k Combine like terms: 9k + -9k = 0 4 + -15k = -4 + 0 4 + -15k = -4 Add '-4' to each side of the equation. 4 + -4 + -15k = -4 + -4 Combine like terms: 4 + -4 = 0 0 + -15k = -4 + -4 -15k = -4 + -4 Combine like terms: -4 + -4 = -8 -15k = -8 Divide each side by '-15'. k = 0.5333333333 Simplifying k = 0.5333333333
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