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Simplifying 3w + -6 + 3n = 8n + -3(n + -4) Reorder the terms: -6 + 3n + 3w = 8n + -3(n + -4) Reorder the terms: -6 + 3n + 3w = 8n + -3(-4 + n) -6 + 3n + 3w = 8n + (-4 * -3 + n * -3) -6 + 3n + 3w = 8n + (12 + -3n) Reorder the terms: -6 + 3n + 3w = 12 + 8n + -3n Combine like terms: 8n + -3n = 5n -6 + 3n + 3w = 12 + 5n Solving -6 + 3n + 3w = 12 + 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. -6 + 3n + -5n + 3w = 12 + 5n + -5n Combine like terms: 3n + -5n = -2n -6 + -2n + 3w = 12 + 5n + -5n Combine like terms: 5n + -5n = 0 -6 + -2n + 3w = 12 + 0 -6 + -2n + 3w = 12 Add '6' to each side of the equation. -6 + -2n + 6 + 3w = 12 + 6 Reorder the terms: -6 + 6 + -2n + 3w = 12 + 6 Combine like terms: -6 + 6 = 0 0 + -2n + 3w = 12 + 6 -2n + 3w = 12 + 6 Combine like terms: 12 + 6 = 18 -2n + 3w = 18 Add '-3w' to each side of the equation. -2n + 3w + -3w = 18 + -3w Combine like terms: 3w + -3w = 0 -2n + 0 = 18 + -3w -2n = 18 + -3w Divide each side by '-2'. n = -9 + 1.5w Simplifying n = -9 + 1.5w
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