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Simplifying 12n + 5 + 11 + n = -5(1 + -6n) + -2(9n + 1) Reorder the terms: 5 + 11 + 12n + n = -5(1 + -6n) + -2(9n + 1) Combine like terms: 5 + 11 = 16 16 + 12n + n = -5(1 + -6n) + -2(9n + 1) Combine like terms: 12n + n = 13n 16 + 13n = -5(1 + -6n) + -2(9n + 1) 16 + 13n = (1 * -5 + -6n * -5) + -2(9n + 1) 16 + 13n = (-5 + 30n) + -2(9n + 1) Reorder the terms: 16 + 13n = -5 + 30n + -2(1 + 9n) 16 + 13n = -5 + 30n + (1 * -2 + 9n * -2) 16 + 13n = -5 + 30n + (-2 + -18n) Reorder the terms: 16 + 13n = -5 + -2 + 30n + -18n Combine like terms: -5 + -2 = -7 16 + 13n = -7 + 30n + -18n Combine like terms: 30n + -18n = 12n 16 + 13n = -7 + 12n Solving 16 + 13n = -7 + 12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-12n' to each side of the equation. 16 + 13n + -12n = -7 + 12n + -12n Combine like terms: 13n + -12n = 1n 16 + 1n = -7 + 12n + -12n Combine like terms: 12n + -12n = 0 16 + 1n = -7 + 0 16 + 1n = -7 Add '-16' to each side of the equation. 16 + -16 + 1n = -7 + -16 Combine like terms: 16 + -16 = 0 0 + 1n = -7 + -16 1n = -7 + -16 Combine like terms: -7 + -16 = -23 1n = -23 Divide each side by '1'. n = -23 Simplifying n = -23
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