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Simplifying 11n + 11 + -2 = 4(10n + -7) + -9(1 + 3n) Reorder the terms: 11 + -2 + 11n = 4(10n + -7) + -9(1 + 3n) Combine like terms: 11 + -2 = 9 9 + 11n = 4(10n + -7) + -9(1 + 3n) Reorder the terms: 9 + 11n = 4(-7 + 10n) + -9(1 + 3n) 9 + 11n = (-7 * 4 + 10n * 4) + -9(1 + 3n) 9 + 11n = (-28 + 40n) + -9(1 + 3n) 9 + 11n = -28 + 40n + (1 * -9 + 3n * -9) 9 + 11n = -28 + 40n + (-9 + -27n) Reorder the terms: 9 + 11n = -28 + -9 + 40n + -27n Combine like terms: -28 + -9 = -37 9 + 11n = -37 + 40n + -27n Combine like terms: 40n + -27n = 13n 9 + 11n = -37 + 13n Solving 9 + 11n = -37 + 13n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13n' to each side of the equation. 9 + 11n + -13n = -37 + 13n + -13n Combine like terms: 11n + -13n = -2n 9 + -2n = -37 + 13n + -13n Combine like terms: 13n + -13n = 0 9 + -2n = -37 + 0 9 + -2n = -37 Add '-9' to each side of the equation. 9 + -9 + -2n = -37 + -9 Combine like terms: 9 + -9 = 0 0 + -2n = -37 + -9 -2n = -37 + -9 Combine like terms: -37 + -9 = -46 -2n = -46 Divide each side by '-2'. n = 23 Simplifying n = 23
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