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Simplifying 0.5(3n + 6) = 5n + -12 + -1n Reorder the terms: 0.5(6 + 3n) = 5n + -12 + -1n (6 * 0.5 + 3n * 0.5) = 5n + -12 + -1n (3 + 1.5n) = 5n + -12 + -1n Reorder the terms: 3 + 1.5n = -12 + 5n + -1n Combine like terms: 5n + -1n = 4n 3 + 1.5n = -12 + 4n Solving 3 + 1.5n = -12 + 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. 3 + 1.5n + -4n = -12 + 4n + -4n Combine like terms: 1.5n + -4n = -2.5n 3 + -2.5n = -12 + 4n + -4n Combine like terms: 4n + -4n = 0 3 + -2.5n = -12 + 0 3 + -2.5n = -12 Add '-3' to each side of the equation. 3 + -3 + -2.5n = -12 + -3 Combine like terms: 3 + -3 = 0 0 + -2.5n = -12 + -3 -2.5n = -12 + -3 Combine like terms: -12 + -3 = -15 -2.5n = -15 Divide each side by '-2.5'. n = 6 Simplifying n = 6
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