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Simplifying 10n + 9 + -17 + -1n = 2(2n + 4) + -3(2n + -2) Reorder the terms: 9 + -17 + 10n + -1n = 2(2n + 4) + -3(2n + -2) Combine like terms: 9 + -17 = -8 -8 + 10n + -1n = 2(2n + 4) + -3(2n + -2) Combine like terms: 10n + -1n = 9n -8 + 9n = 2(2n + 4) + -3(2n + -2) Reorder the terms: -8 + 9n = 2(4 + 2n) + -3(2n + -2) -8 + 9n = (4 * 2 + 2n * 2) + -3(2n + -2) -8 + 9n = (8 + 4n) + -3(2n + -2) Reorder the terms: -8 + 9n = 8 + 4n + -3(-2 + 2n) -8 + 9n = 8 + 4n + (-2 * -3 + 2n * -3) -8 + 9n = 8 + 4n + (6 + -6n) Reorder the terms: -8 + 9n = 8 + 6 + 4n + -6n Combine like terms: 8 + 6 = 14 -8 + 9n = 14 + 4n + -6n Combine like terms: 4n + -6n = -2n -8 + 9n = 14 + -2n Solving -8 + 9n = 14 + -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. -8 + 9n + 2n = 14 + -2n + 2n Combine like terms: 9n + 2n = 11n -8 + 11n = 14 + -2n + 2n Combine like terms: -2n + 2n = 0 -8 + 11n = 14 + 0 -8 + 11n = 14 Add '8' to each side of the equation. -8 + 8 + 11n = 14 + 8 Combine like terms: -8 + 8 = 0 0 + 11n = 14 + 8 11n = 14 + 8 Combine like terms: 14 + 8 = 22 11n = 22 Divide each side by '11'. n = 2 Simplifying n = 2
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