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Simplifying 3n + 8 = 2(n + -4) + -2(1 + -1n) Reorder the terms: 8 + 3n = 2(n + -4) + -2(1 + -1n) Reorder the terms: 8 + 3n = 2(-4 + n) + -2(1 + -1n) 8 + 3n = (-4 * 2 + n * 2) + -2(1 + -1n) 8 + 3n = (-8 + 2n) + -2(1 + -1n) 8 + 3n = -8 + 2n + (1 * -2 + -1n * -2) 8 + 3n = -8 + 2n + (-2 + 2n) Reorder the terms: 8 + 3n = -8 + -2 + 2n + 2n Combine like terms: -8 + -2 = -10 8 + 3n = -10 + 2n + 2n Combine like terms: 2n + 2n = 4n 8 + 3n = -10 + 4n Solving 8 + 3n = -10 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. 8 + 3n + -4n = -10 + 4n + -4n Combine like terms: 3n + -4n = -1n 8 + -1n = -10 + 4n + -4n Combine like terms: 4n + -4n = 0 8 + -1n = -10 + 0 8 + -1n = -10 Add '-8' to each side of the equation. 8 + -8 + -1n = -10 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = -10 + -8 -1n = -10 + -8 Combine like terms: -10 + -8 = -18 -1n = -18 Divide each side by '-1'. n = 18 Simplifying n = 18
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