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Simplifying 7 = (1 + 5n) + 6(k + 5) Remove parenthesis around (1 + 5n) 7 = 1 + 5n + 6(k + 5) Reorder the terms: 7 = 1 + 5n + 6(5 + k) 7 = 1 + 5n + (5 * 6 + k * 6) 7 = 1 + 5n + (30 + 6k) Reorder the terms: 7 = 1 + 30 + 6k + 5n Combine like terms: 1 + 30 = 31 7 = 31 + 6k + 5n Solving 7 = 31 + 6k + 5n Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 7 + -6k = 31 + 6k + -6k + 5n Combine like terms: 6k + -6k = 0 7 + -6k = 31 + 0 + 5n 7 + -6k = 31 + 5n Add '-7' to each side of the equation. 7 + -7 + -6k = 31 + -7 + 5n Combine like terms: 7 + -7 = 0 0 + -6k = 31 + -7 + 5n -6k = 31 + -7 + 5n Combine like terms: 31 + -7 = 24 -6k = 24 + 5n Divide each side by '-6'. k = -4 + -0.8333333333n Simplifying k = -4 + -0.8333333333n
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