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Simplifying 1 + n + 4n = -3(1 + n) + -4(n + -1) Combine like terms: n + 4n = 5n 1 + 5n = -3(1 + n) + -4(n + -1) 1 + 5n = (1 * -3 + n * -3) + -4(n + -1) 1 + 5n = (-3 + -3n) + -4(n + -1) Reorder the terms: 1 + 5n = -3 + -3n + -4(-1 + n) 1 + 5n = -3 + -3n + (-1 * -4 + n * -4) 1 + 5n = -3 + -3n + (4 + -4n) Reorder the terms: 1 + 5n = -3 + 4 + -3n + -4n Combine like terms: -3 + 4 = 1 1 + 5n = 1 + -3n + -4n Combine like terms: -3n + -4n = -7n 1 + 5n = 1 + -7n Add '-1' to each side of the equation. 1 + -1 + 5n = 1 + -1 + -7n Combine like terms: 1 + -1 = 0 0 + 5n = 1 + -1 + -7n 5n = 1 + -1 + -7n Combine like terms: 1 + -1 = 0 5n = 0 + -7n 5n = -7n Solving 5n = -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. 5n + 7n = -7n + 7n Combine like terms: 5n + 7n = 12n 12n = -7n + 7n Combine like terms: -7n + 7n = 0 12n = 0 Divide each side by '12'. n = 0 Simplifying n = 0
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