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Simplifying 7(3n + 5) = 6(2n + 3) + 1 Reorder the terms: 7(5 + 3n) = 6(2n + 3) + 1 (5 * 7 + 3n * 7) = 6(2n + 3) + 1 (35 + 21n) = 6(2n + 3) + 1 Reorder the terms: 35 + 21n = 6(3 + 2n) + 1 35 + 21n = (3 * 6 + 2n * 6) + 1 35 + 21n = (18 + 12n) + 1 Reorder the terms: 35 + 21n = 18 + 1 + 12n Combine like terms: 18 + 1 = 19 35 + 21n = 19 + 12n Solving 35 + 21n = 19 + 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. 35 + 21n + -12n = 19 + 12n + -12n Combine like terms: 21n + -12n = 9n 35 + 9n = 19 + 12n + -12n Combine like terms: 12n + -12n = 0 35 + 9n = 19 + 0 35 + 9n = 19 Add '-35' to each side of the equation. 35 + -35 + 9n = 19 + -35 Combine like terms: 35 + -35 = 0 0 + 9n = 19 + -35 9n = 19 + -35 Combine like terms: 19 + -35 = -16 9n = -16 Divide each side by '9'. n = -1.777777778 Simplifying n = -1.777777778
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