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Simplifying -1(1 + 6k) + 4k = -8k + -7(k + 2) (1 * -1 + 6k * -1) + 4k = -8k + -7(k + 2) (-1 + -6k) + 4k = -8k + -7(k + 2) Combine like terms: -6k + 4k = -2k -1 + -2k = -8k + -7(k + 2) Reorder the terms: -1 + -2k = -8k + -7(2 + k) -1 + -2k = -8k + (2 * -7 + k * -7) -1 + -2k = -8k + (-14 + -7k) Reorder the terms: -1 + -2k = -14 + -8k + -7k Combine like terms: -8k + -7k = -15k -1 + -2k = -14 + -15k Solving -1 + -2k = -14 + -15k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '15k' to each side of the equation. -1 + -2k + 15k = -14 + -15k + 15k Combine like terms: -2k + 15k = 13k -1 + 13k = -14 + -15k + 15k Combine like terms: -15k + 15k = 0 -1 + 13k = -14 + 0 -1 + 13k = -14 Add '1' to each side of the equation. -1 + 1 + 13k = -14 + 1 Combine like terms: -1 + 1 = 0 0 + 13k = -14 + 1 13k = -14 + 1 Combine like terms: -14 + 1 = -13 13k = -13 Divide each side by '13'. k = -1 Simplifying k = -1
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