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Simplifying 6 + 2n + 10 + 2n = 2(1 + -5n) + -2(10 + 10n) Reorder the terms: 6 + 10 + 2n + 2n = 2(1 + -5n) + -2(10 + 10n) Combine like terms: 6 + 10 = 16 16 + 2n + 2n = 2(1 + -5n) + -2(10 + 10n) Combine like terms: 2n + 2n = 4n 16 + 4n = 2(1 + -5n) + -2(10 + 10n) 16 + 4n = (1 * 2 + -5n * 2) + -2(10 + 10n) 16 + 4n = (2 + -10n) + -2(10 + 10n) 16 + 4n = 2 + -10n + (10 * -2 + 10n * -2) 16 + 4n = 2 + -10n + (-20 + -20n) Reorder the terms: 16 + 4n = 2 + -20 + -10n + -20n Combine like terms: 2 + -20 = -18 16 + 4n = -18 + -10n + -20n Combine like terms: -10n + -20n = -30n 16 + 4n = -18 + -30n Solving 16 + 4n = -18 + -30n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '30n' to each side of the equation. 16 + 4n + 30n = -18 + -30n + 30n Combine like terms: 4n + 30n = 34n 16 + 34n = -18 + -30n + 30n Combine like terms: -30n + 30n = 0 16 + 34n = -18 + 0 16 + 34n = -18 Add '-16' to each side of the equation. 16 + -16 + 34n = -18 + -16 Combine like terms: 16 + -16 = 0 0 + 34n = -18 + -16 34n = -18 + -16 Combine like terms: -18 + -16 = -34 34n = -34 Divide each side by '34'. n = -1 Simplifying n = -1
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