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Simplifying 4(5 + 3n) + -1 = 4(n + 1) + 3n (5 * 4 + 3n * 4) + -1 = 4(n + 1) + 3n (20 + 12n) + -1 = 4(n + 1) + 3n Reorder the terms: 20 + -1 + 12n = 4(n + 1) + 3n Combine like terms: 20 + -1 = 19 19 + 12n = 4(n + 1) + 3n Reorder the terms: 19 + 12n = 4(1 + n) + 3n 19 + 12n = (1 * 4 + n * 4) + 3n 19 + 12n = (4 + 4n) + 3n Combine like terms: 4n + 3n = 7n 19 + 12n = 4 + 7n Solving 19 + 12n = 4 + 7n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7n' to each side of the equation. 19 + 12n + -7n = 4 + 7n + -7n Combine like terms: 12n + -7n = 5n 19 + 5n = 4 + 7n + -7n Combine like terms: 7n + -7n = 0 19 + 5n = 4 + 0 19 + 5n = 4 Add '-19' to each side of the equation. 19 + -19 + 5n = 4 + -19 Combine like terms: 19 + -19 = 0 0 + 5n = 4 + -19 5n = 4 + -19 Combine like terms: 4 + -19 = -15 5n = -15 Divide each side by '5'. n = -3 Simplifying n = -3
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