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Simplifying 18 = 10(1 + -9n) + 2(4 + 5n) 18 = (1 * 10 + -9n * 10) + 2(4 + 5n) 18 = (10 + -90n) + 2(4 + 5n) 18 = 10 + -90n + (4 * 2 + 5n * 2) 18 = 10 + -90n + (8 + 10n) Reorder the terms: 18 = 10 + 8 + -90n + 10n Combine like terms: 10 + 8 = 18 18 = 18 + -90n + 10n Combine like terms: -90n + 10n = -80n 18 = 18 + -80n Add '-18' to each side of the equation. 18 + -18 = 18 + -18 + -80n Combine like terms: 18 + -18 = 0 0 = 18 + -18 + -80n Combine like terms: 18 + -18 = 0 0 = 0 + -80n 0 = -80n Solving 0 = -80n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '80n' to each side of the equation. 0 + 80n = -80n + 80n Remove the zero: 80n = -80n + 80n Combine like terms: -80n + 80n = 0 80n = 0 Divide each side by '80'. n = 0 Simplifying n = 0
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