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Simplifying (k + 1) + 5k = -1 + 5(k + -1) Reorder the terms: (1 + k) + 5k = -1 + 5(k + -1) Remove parenthesis around (1 + k) 1 + k + 5k = -1 + 5(k + -1) Combine like terms: k + 5k = 6k 1 + 6k = -1 + 5(k + -1) Reorder the terms: 1 + 6k = -1 + 5(-1 + k) 1 + 6k = -1 + (-1 * 5 + k * 5) 1 + 6k = -1 + (-5 + 5k) Combine like terms: -1 + -5 = -6 1 + 6k = -6 + 5k Solving 1 + 6k = -6 + 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. 1 + 6k + -5k = -6 + 5k + -5k Combine like terms: 6k + -5k = 1k 1 + 1k = -6 + 5k + -5k Combine like terms: 5k + -5k = 0 1 + 1k = -6 + 0 1 + 1k = -6 Add '-1' to each side of the equation. 1 + -1 + 1k = -6 + -1 Combine like terms: 1 + -1 = 0 0 + 1k = -6 + -1 1k = -6 + -1 Combine like terms: -6 + -1 = -7 1k = -7 Divide each side by '1'. k = -7 Simplifying k = -7
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