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Simplifying 11n + 11 + 2n + 8 = 6(n + 5) + 3(7 + 3n) Reorder the terms: 11 + 8 + 11n + 2n = 6(n + 5) + 3(7 + 3n) Combine like terms: 11 + 8 = 19 19 + 11n + 2n = 6(n + 5) + 3(7 + 3n) Combine like terms: 11n + 2n = 13n 19 + 13n = 6(n + 5) + 3(7 + 3n) Reorder the terms: 19 + 13n = 6(5 + n) + 3(7 + 3n) 19 + 13n = (5 * 6 + n * 6) + 3(7 + 3n) 19 + 13n = (30 + 6n) + 3(7 + 3n) 19 + 13n = 30 + 6n + (7 * 3 + 3n * 3) 19 + 13n = 30 + 6n + (21 + 9n) Reorder the terms: 19 + 13n = 30 + 21 + 6n + 9n Combine like terms: 30 + 21 = 51 19 + 13n = 51 + 6n + 9n Combine like terms: 6n + 9n = 15n 19 + 13n = 51 + 15n Solving 19 + 13n = 51 + 15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15n' to each side of the equation. 19 + 13n + -15n = 51 + 15n + -15n Combine like terms: 13n + -15n = -2n 19 + -2n = 51 + 15n + -15n Combine like terms: 15n + -15n = 0 19 + -2n = 51 + 0 19 + -2n = 51 Add '-19' to each side of the equation. 19 + -19 + -2n = 51 + -19 Combine like terms: 19 + -19 = 0 0 + -2n = 51 + -19 -2n = 51 + -19 Combine like terms: 51 + -19 = 32 -2n = 32 Divide each side by '-2'. n = -16 Simplifying n = -16
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