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Simplifying 6(1 + k) + 1 = 23 + 8k (1 * 6 + k * 6) + 1 = 23 + 8k (6 + 6k) + 1 = 23 + 8k Reorder the terms: 6 + 1 + 6k = 23 + 8k Combine like terms: 6 + 1 = 7 7 + 6k = 23 + 8k Solving 7 + 6k = 23 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 7 + 6k + -8k = 23 + 8k + -8k Combine like terms: 6k + -8k = -2k 7 + -2k = 23 + 8k + -8k Combine like terms: 8k + -8k = 0 7 + -2k = 23 + 0 7 + -2k = 23 Add '-7' to each side of the equation. 7 + -7 + -2k = 23 + -7 Combine like terms: 7 + -7 = 0 0 + -2k = 23 + -7 -2k = 23 + -7 Combine like terms: 23 + -7 = 16 -2k = 16 Divide each side by '-2'. k = -8 Simplifying k = -8
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