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Simplifying 0.5(10 + 12n) = 0.3333(15n + 15) (10 * 0.5 + 12n * 0.5) = 0.3333(15n + 15) (5 + 6n) = 0.3333(15n + 15) Reorder the terms: 5 + 6n = 0.3333(15 + 15n) 5 + 6n = (15 * 0.3333 + 15n * 0.3333) 5 + 6n = (4.9995 + 4.9995n) Solving 5 + 6n = 4.9995 + 4.9995n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.9995n' to each side of the equation. 5 + 6n + -4.9995n = 4.9995 + 4.9995n + -4.9995n Combine like terms: 6n + -4.9995n = 1.0005n 5 + 1.0005n = 4.9995 + 4.9995n + -4.9995n Combine like terms: 4.9995n + -4.9995n = 0.0000 5 + 1.0005n = 4.9995 + 0.0000 5 + 1.0005n = 4.9995 Add '-5' to each side of the equation. 5 + -5 + 1.0005n = 4.9995 + -5 Combine like terms: 5 + -5 = 0 0 + 1.0005n = 4.9995 + -5 1.0005n = 4.9995 + -5 Combine like terms: 4.9995 + -5 = -0.0005 1.0005n = -0.0005 Divide each side by '1.0005'. n = -0.0004997501249 Simplifying n = -0.0004997501249
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