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Simplifying 0.12(3n + -9) + -1n = 0.27(8 + -2n) Reorder the terms: 0.12(-9 + 3n) + -1n = 0.27(8 + -2n) (-9 * 0.12 + 3n * 0.12) + -1n = 0.27(8 + -2n) (-1.08 + 0.36n) + -1n = 0.27(8 + -2n) Combine like terms: 0.36n + -1n = -0.64n -1.08 + -0.64n = 0.27(8 + -2n) -1.08 + -0.64n = (8 * 0.27 + -2n * 0.27) -1.08 + -0.64n = (2.16 + -0.54n) Solving -1.08 + -0.64n = 2.16 + -0.54n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.54n' to each side of the equation. -1.08 + -0.64n + 0.54n = 2.16 + -0.54n + 0.54n Combine like terms: -0.64n + 0.54n = -0.1n -1.08 + -0.1n = 2.16 + -0.54n + 0.54n Combine like terms: -0.54n + 0.54n = 0.00 -1.08 + -0.1n = 2.16 + 0.00 -1.08 + -0.1n = 2.16 Add '1.08' to each side of the equation. -1.08 + 1.08 + -0.1n = 2.16 + 1.08 Combine like terms: -1.08 + 1.08 = 0.00 0.00 + -0.1n = 2.16 + 1.08 -0.1n = 2.16 + 1.08 Combine like terms: 2.16 + 1.08 = 3.24 -0.1n = 3.24 Divide each side by '-0.1'. n = -32.4 Simplifying n = -32.4
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