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Simplifying 3n + -1 + -1(n + -4) + -1[2(n + -3) + -3(1 + -2n)] = -1n + -2 Reorder the terms: 3n + -1 + -1(-4 + n) + -1[2(n + -3) + -3(1 + -2n)] = -1n + -2 3n + -1 + (-4 * -1 + n * -1) + -1[2(n + -3) + -3(1 + -2n)] = -1n + -2 3n + -1 + (4 + -1n) + -1[2(n + -3) + -3(1 + -2n)] = -1n + -2 Reorder the terms: 3n + -1 + 4 + -1n + -1[2(-3 + n) + -3(1 + -2n)] = -1n + -2 3n + -1 + 4 + -1n + -1[(-3 * 2 + n * 2) + -3(1 + -2n)] = -1n + -2 3n + -1 + 4 + -1n + -1[(-6 + 2n) + -3(1 + -2n)] = -1n + -2 3n + -1 + 4 + -1n + -1[-6 + 2n + (1 * -3 + -2n * -3)] = -1n + -2 3n + -1 + 4 + -1n + -1[-6 + 2n + (-3 + 6n)] = -1n + -2 Reorder the terms: 3n + -1 + 4 + -1n + -1[-6 + -3 + 2n + 6n] = -1n + -2 Combine like terms: -6 + -3 = -9 3n + -1 + 4 + -1n + -1[-9 + 2n + 6n] = -1n + -2 Combine like terms: 2n + 6n = 8n 3n + -1 + 4 + -1n + -1[-9 + 8n] = -1n + -2 3n + -1 + 4 + -1n + [-9 * -1 + 8n * -1] = -1n + -2 3n + -1 + 4 + -1n + [9 + -8n] = -1n + -2 Reorder the terms: -1 + 4 + 9 + 3n + -1n + -8n = -1n + -2 Combine like terms: -1 + 4 = 3 3 + 9 + 3n + -1n + -8n = -1n + -2 Combine like terms: 3 + 9 = 12 12 + 3n + -1n + -8n = -1n + -2 Combine like terms: 3n + -1n = 2n 12 + 2n + -8n = -1n + -2 Combine like terms: 2n + -8n = -6n 12 + -6n = -1n + -2 Reorder the terms: 12 + -6n = -2 + -1n Solving 12 + -6n = -2 + -1n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add 'n' to each side of the equation. 12 + -6n + n = -2 + -1n + n Combine like terms: -6n + n = -5n 12 + -5n = -2 + -1n + n Combine like terms: -1n + n = 0 12 + -5n = -2 + 0 12 + -5n = -2 Add '-12' to each side of the equation. 12 + -12 + -5n = -2 + -12 Combine like terms: 12 + -12 = 0 0 + -5n = -2 + -12 -5n = -2 + -12 Combine like terms: -2 + -12 = -14 -5n = -14 Divide each side by '-5'. n = 2.8 Simplifying n = 2.8
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