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Simplifying 2(4 + -3k) + 6 = 5(-2 + 7k) + 3k (4 * 2 + -3k * 2) + 6 = 5(-2 + 7k) + 3k (8 + -6k) + 6 = 5(-2 + 7k) + 3k Reorder the terms: 8 + 6 + -6k = 5(-2 + 7k) + 3k Combine like terms: 8 + 6 = 14 14 + -6k = 5(-2 + 7k) + 3k 14 + -6k = (-2 * 5 + 7k * 5) + 3k 14 + -6k = (-10 + 35k) + 3k Combine like terms: 35k + 3k = 38k 14 + -6k = -10 + 38k Solving 14 + -6k = -10 + 38k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-38k' to each side of the equation. 14 + -6k + -38k = -10 + 38k + -38k Combine like terms: -6k + -38k = -44k 14 + -44k = -10 + 38k + -38k Combine like terms: 38k + -38k = 0 14 + -44k = -10 + 0 14 + -44k = -10 Add '-14' to each side of the equation. 14 + -14 + -44k = -10 + -14 Combine like terms: 14 + -14 = 0 0 + -44k = -10 + -14 -44k = -10 + -14 Combine like terms: -10 + -14 = -24 -44k = -24 Divide each side by '-44'. k = 0.5454545455 Simplifying k = 0.5454545455
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