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Simplifying 9n + -12 + 10n + 8 = 2(3 + -7n) + 4(4n + 6) Reorder the terms: -12 + 8 + 9n + 10n = 2(3 + -7n) + 4(4n + 6) Combine like terms: -12 + 8 = -4 -4 + 9n + 10n = 2(3 + -7n) + 4(4n + 6) Combine like terms: 9n + 10n = 19n -4 + 19n = 2(3 + -7n) + 4(4n + 6) -4 + 19n = (3 * 2 + -7n * 2) + 4(4n + 6) -4 + 19n = (6 + -14n) + 4(4n + 6) Reorder the terms: -4 + 19n = 6 + -14n + 4(6 + 4n) -4 + 19n = 6 + -14n + (6 * 4 + 4n * 4) -4 + 19n = 6 + -14n + (24 + 16n) Reorder the terms: -4 + 19n = 6 + 24 + -14n + 16n Combine like terms: 6 + 24 = 30 -4 + 19n = 30 + -14n + 16n Combine like terms: -14n + 16n = 2n -4 + 19n = 30 + 2n Solving -4 + 19n = 30 + 2n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2n' to each side of the equation. -4 + 19n + -2n = 30 + 2n + -2n Combine like terms: 19n + -2n = 17n -4 + 17n = 30 + 2n + -2n Combine like terms: 2n + -2n = 0 -4 + 17n = 30 + 0 -4 + 17n = 30 Add '4' to each side of the equation. -4 + 4 + 17n = 30 + 4 Combine like terms: -4 + 4 = 0 0 + 17n = 30 + 4 17n = 30 + 4 Combine like terms: 30 + 4 = 34 17n = 34 Divide each side by '17'. n = 2 Simplifying n = 2
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