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Simplifying 2(k + -1) = 4k + -7(k + 6) Reorder the terms: 2(-1 + k) = 4k + -7(k + 6) (-1 * 2 + k * 2) = 4k + -7(k + 6) (-2 + 2k) = 4k + -7(k + 6) Reorder the terms: -2 + 2k = 4k + -7(6 + k) -2 + 2k = 4k + (6 * -7 + k * -7) -2 + 2k = 4k + (-42 + -7k) Reorder the terms: -2 + 2k = -42 + 4k + -7k Combine like terms: 4k + -7k = -3k -2 + 2k = -42 + -3k Solving -2 + 2k = -42 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. -2 + 2k + 3k = -42 + -3k + 3k Combine like terms: 2k + 3k = 5k -2 + 5k = -42 + -3k + 3k Combine like terms: -3k + 3k = 0 -2 + 5k = -42 + 0 -2 + 5k = -42 Add '2' to each side of the equation. -2 + 2 + 5k = -42 + 2 Combine like terms: -2 + 2 = 0 0 + 5k = -42 + 2 5k = -42 + 2 Combine like terms: -42 + 2 = -40 5k = -40 Divide each side by '5'. k = -8 Simplifying k = -8
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