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Simplifying -77 = 7(n + 6) + 7(1 + 5n) Reorder the terms: -77 = 7(6 + n) + 7(1 + 5n) -77 = (6 * 7 + n * 7) + 7(1 + 5n) -77 = (42 + 7n) + 7(1 + 5n) -77 = 42 + 7n + (1 * 7 + 5n * 7) -77 = 42 + 7n + (7 + 35n) Reorder the terms: -77 = 42 + 7 + 7n + 35n Combine like terms: 42 + 7 = 49 -77 = 49 + 7n + 35n Combine like terms: 7n + 35n = 42n -77 = 49 + 42n Solving -77 = 49 + 42n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-42n' to each side of the equation. -77 + -42n = 49 + 42n + -42n Combine like terms: 42n + -42n = 0 -77 + -42n = 49 + 0 -77 + -42n = 49 Add '77' to each side of the equation. -77 + 77 + -42n = 49 + 77 Combine like terms: -77 + 77 = 0 0 + -42n = 49 + 77 -42n = 49 + 77 Combine like terms: 49 + 77 = 126 -42n = 126 Divide each side by '-42'. n = -3 Simplifying n = -3
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