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Simplifying 14 + -1(6 + -6n) + 21 = -14 + 24(n + 1) 14 + (6 * -1 + -6n * -1) + 21 = -14 + 24(n + 1) 14 + (-6 + 6n) + 21 = -14 + 24(n + 1) Reorder the terms: 14 + -6 + 21 + 6n = -14 + 24(n + 1) Combine like terms: 14 + -6 = 8 8 + 21 + 6n = -14 + 24(n + 1) Combine like terms: 8 + 21 = 29 29 + 6n = -14 + 24(n + 1) Reorder the terms: 29 + 6n = -14 + 24(1 + n) 29 + 6n = -14 + (1 * 24 + n * 24) 29 + 6n = -14 + (24 + 24n) Combine like terms: -14 + 24 = 10 29 + 6n = 10 + 24n Solving 29 + 6n = 10 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. 29 + 6n + -24n = 10 + 24n + -24n Combine like terms: 6n + -24n = -18n 29 + -18n = 10 + 24n + -24n Combine like terms: 24n + -24n = 0 29 + -18n = 10 + 0 29 + -18n = 10 Add '-29' to each side of the equation. 29 + -29 + -18n = 10 + -29 Combine like terms: 29 + -29 = 0 0 + -18n = 10 + -29 -18n = 10 + -29 Combine like terms: 10 + -29 = -19 -18n = -19 Divide each side by '-18'. n = 1.055555556 Simplifying n = 1.055555556
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