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Simplifying 6(1 + -4v) + 3(5n + 7) = 1 + -5n + -2 (1 * 6 + -4v * 6) + 3(5n + 7) = 1 + -5n + -2 (6 + -24v) + 3(5n + 7) = 1 + -5n + -2 Reorder the terms: 6 + -24v + 3(7 + 5n) = 1 + -5n + -2 6 + -24v + (7 * 3 + 5n * 3) = 1 + -5n + -2 6 + -24v + (21 + 15n) = 1 + -5n + -2 Reorder the terms: 6 + 21 + 15n + -24v = 1 + -5n + -2 Combine like terms: 6 + 21 = 27 27 + 15n + -24v = 1 + -5n + -2 Reorder the terms: 27 + 15n + -24v = 1 + -2 + -5n Combine like terms: 1 + -2 = -1 27 + 15n + -24v = -1 + -5n Solving 27 + 15n + -24v = -1 + -5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5n' to each side of the equation. 27 + 15n + 5n + -24v = -1 + -5n + 5n Combine like terms: 15n + 5n = 20n 27 + 20n + -24v = -1 + -5n + 5n Combine like terms: -5n + 5n = 0 27 + 20n + -24v = -1 + 0 27 + 20n + -24v = -1 Add '-27' to each side of the equation. 27 + 20n + -27 + -24v = -1 + -27 Reorder the terms: 27 + -27 + 20n + -24v = -1 + -27 Combine like terms: 27 + -27 = 0 0 + 20n + -24v = -1 + -27 20n + -24v = -1 + -27 Combine like terms: -1 + -27 = -28 20n + -24v = -28 Add '24v' to each side of the equation. 20n + -24v + 24v = -28 + 24v Combine like terms: -24v + 24v = 0 20n + 0 = -28 + 24v 20n = -28 + 24v Divide each side by '20'. n = -1.4 + 1.2v Simplifying n = -1.4 + 1.2v
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