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Simplifying 5n + 4(n + -2) + -2n = 2(n + -1) + 3(n + 2) Reorder the terms: 5n + 4(-2 + n) + -2n = 2(n + -1) + 3(n + 2) 5n + (-2 * 4 + n * 4) + -2n = 2(n + -1) + 3(n + 2) 5n + (-8 + 4n) + -2n = 2(n + -1) + 3(n + 2) Reorder the terms: -8 + 5n + 4n + -2n = 2(n + -1) + 3(n + 2) Combine like terms: 5n + 4n = 9n -8 + 9n + -2n = 2(n + -1) + 3(n + 2) Combine like terms: 9n + -2n = 7n -8 + 7n = 2(n + -1) + 3(n + 2) Reorder the terms: -8 + 7n = 2(-1 + n) + 3(n + 2) -8 + 7n = (-1 * 2 + n * 2) + 3(n + 2) -8 + 7n = (-2 + 2n) + 3(n + 2) Reorder the terms: -8 + 7n = -2 + 2n + 3(2 + n) -8 + 7n = -2 + 2n + (2 * 3 + n * 3) -8 + 7n = -2 + 2n + (6 + 3n) Reorder the terms: -8 + 7n = -2 + 6 + 2n + 3n Combine like terms: -2 + 6 = 4 -8 + 7n = 4 + 2n + 3n Combine like terms: 2n + 3n = 5n -8 + 7n = 4 + 5n Solving -8 + 7n = 4 + 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. -8 + 7n + -5n = 4 + 5n + -5n Combine like terms: 7n + -5n = 2n -8 + 2n = 4 + 5n + -5n Combine like terms: 5n + -5n = 0 -8 + 2n = 4 + 0 -8 + 2n = 4 Add '8' to each side of the equation. -8 + 8 + 2n = 4 + 8 Combine like terms: -8 + 8 = 0 0 + 2n = 4 + 8 2n = 4 + 8 Combine like terms: 4 + 8 = 12 2n = 12 Divide each side by '2'. n = 6 Simplifying n = 6
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