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Simplifying 7(2 + n) + -2(3n + 1) = 10(n + 3) (2 * 7 + n * 7) + -2(3n + 1) = 10(n + 3) (14 + 7n) + -2(3n + 1) = 10(n + 3) Reorder the terms: 14 + 7n + -2(1 + 3n) = 10(n + 3) 14 + 7n + (1 * -2 + 3n * -2) = 10(n + 3) 14 + 7n + (-2 + -6n) = 10(n + 3) Reorder the terms: 14 + -2 + 7n + -6n = 10(n + 3) Combine like terms: 14 + -2 = 12 12 + 7n + -6n = 10(n + 3) Combine like terms: 7n + -6n = 1n 12 + 1n = 10(n + 3) Reorder the terms: 12 + 1n = 10(3 + n) 12 + 1n = (3 * 10 + n * 10) 12 + 1n = (30 + 10n) Solving 12 + 1n = 30 + 10n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10n' to each side of the equation. 12 + 1n + -10n = 30 + 10n + -10n Combine like terms: 1n + -10n = -9n 12 + -9n = 30 + 10n + -10n Combine like terms: 10n + -10n = 0 12 + -9n = 30 + 0 12 + -9n = 30 Add '-12' to each side of the equation. 12 + -12 + -9n = 30 + -12 Combine like terms: 12 + -12 = 0 0 + -9n = 30 + -12 -9n = 30 + -12 Combine like terms: 30 + -12 = 18 -9n = 18 Divide each side by '-9'. n = -2 Simplifying n = -2
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