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Simplifying in(2) + -1In(3x + 2) = 1 Reorder the terms for easier multiplication: 2in + -1In(3x + 2) = 1 Reorder the terms: 2in + -1nI(2 + 3x) = 1 2in + (2 * -1nI + 3x * -1nI) = 1 2in + (-2nI + -3nxI) = 1 Solving 2in + -2nI + -3nxI = 1 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2nI' to each side of the equation. 2in + -2nI + 2nI + -3nxI = 1 + 2nI Combine like terms: -2nI + 2nI = 0 2in + 0 + -3nxI = 1 + 2nI 2in + -3nxI = 1 + 2nI Add '3nxI' to each side of the equation. 2in + -3nxI + 3nxI = 1 + 2nI + 3nxI Combine like terms: -3nxI + 3nxI = 0 2in + 0 = 1 + 2nI + 3nxI 2in = 1 + 2nI + 3nxI Divide each side by '2n'. i = 0.5n-1 + I + 1.5xI Simplifying i = 0.5n-1 + I + 1.5xI Reorder the terms: i = I + 0.5n-1 + 1.5xI
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