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Simplifying 4(2n + 5) = 6(9n + 7) + 1 Reorder the terms: 4(5 + 2n) = 6(9n + 7) + 1 (5 * 4 + 2n * 4) = 6(9n + 7) + 1 (20 + 8n) = 6(9n + 7) + 1 Reorder the terms: 20 + 8n = 6(7 + 9n) + 1 20 + 8n = (7 * 6 + 9n * 6) + 1 20 + 8n = (42 + 54n) + 1 Reorder the terms: 20 + 8n = 42 + 1 + 54n Combine like terms: 42 + 1 = 43 20 + 8n = 43 + 54n Solving 20 + 8n = 43 + 54n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-54n' to each side of the equation. 20 + 8n + -54n = 43 + 54n + -54n Combine like terms: 8n + -54n = -46n 20 + -46n = 43 + 54n + -54n Combine like terms: 54n + -54n = 0 20 + -46n = 43 + 0 20 + -46n = 43 Add '-20' to each side of the equation. 20 + -20 + -46n = 43 + -20 Combine like terms: 20 + -20 = 0 0 + -46n = 43 + -20 -46n = 43 + -20 Combine like terms: 43 + -20 = 23 -46n = 23 Divide each side by '-46'. n = -0.5 Simplifying n = -0.5
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