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Simplifying -7(k + 5) = 3k + -1(8k + -1) Reorder the terms: -7(5 + k) = 3k + -1(8k + -1) (5 * -7 + k * -7) = 3k + -1(8k + -1) (-35 + -7k) = 3k + -1(8k + -1) Reorder the terms: -35 + -7k = 3k + -1(-1 + 8k) -35 + -7k = 3k + (-1 * -1 + 8k * -1) -35 + -7k = 3k + (1 + -8k) Reorder the terms: -35 + -7k = 1 + 3k + -8k Combine like terms: 3k + -8k = -5k -35 + -7k = 1 + -5k Solving -35 + -7k = 1 + -5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5k' to each side of the equation. -35 + -7k + 5k = 1 + -5k + 5k Combine like terms: -7k + 5k = -2k -35 + -2k = 1 + -5k + 5k Combine like terms: -5k + 5k = 0 -35 + -2k = 1 + 0 -35 + -2k = 1 Add '35' to each side of the equation. -35 + 35 + -2k = 1 + 35 Combine like terms: -35 + 35 = 0 0 + -2k = 1 + 35 -2k = 1 + 35 Combine like terms: 1 + 35 = 36 -2k = 36 Divide each side by '-2'. k = -18 Simplifying k = -18
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