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Simplifying 2n + 6(-5n + 9) = 2(12n + 1) Reorder the terms: 2n + 6(9 + -5n) = 2(12n + 1) 2n + (9 * 6 + -5n * 6) = 2(12n + 1) 2n + (54 + -30n) = 2(12n + 1) Reorder the terms: 54 + 2n + -30n = 2(12n + 1) Combine like terms: 2n + -30n = -28n 54 + -28n = 2(12n + 1) Reorder the terms: 54 + -28n = 2(1 + 12n) 54 + -28n = (1 * 2 + 12n * 2) 54 + -28n = (2 + 24n) Solving 54 + -28n = 2 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. 54 + -28n + -24n = 2 + 24n + -24n Combine like terms: -28n + -24n = -52n 54 + -52n = 2 + 24n + -24n Combine like terms: 24n + -24n = 0 54 + -52n = 2 + 0 54 + -52n = 2 Add '-54' to each side of the equation. 54 + -54 + -52n = 2 + -54 Combine like terms: 54 + -54 = 0 0 + -52n = 2 + -54 -52n = 2 + -54 Combine like terms: 2 + -54 = -52 -52n = -52 Divide each side by '-52'. n = 1 Simplifying n = 1
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