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Simplifying 1 + 5k = 7(2k + 3) + k Reorder the terms: 1 + 5k = 7(3 + 2k) + k 1 + 5k = (3 * 7 + 2k * 7) + k 1 + 5k = (21 + 14k) + k Combine like terms: 14k + k = 15k 1 + 5k = 21 + 15k Solving 1 + 5k = 21 + 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 + 5k + -15k = 21 + 15k + -15k Combine like terms: 5k + -15k = -10k 1 + -10k = 21 + 15k + -15k Combine like terms: 15k + -15k = 0 1 + -10k = 21 + 0 1 + -10k = 21 Add '-1' to each side of the equation. 1 + -1 + -10k = 21 + -1 Combine like terms: 1 + -1 = 0 0 + -10k = 21 + -1 -10k = 21 + -1 Combine like terms: 21 + -1 = 20 -10k = 20 Divide each side by '-10'. k = -2 Simplifying k = -2
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