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Simplifying 3x + 2i(x + 1) = x + 2 + 2i Reorder the terms: 3x + 2i(1 + x) = x + 2 + 2i 3x + (1 * 2i + x * 2i) = x + 2 + 2i 3x + (2i + 2ix) = x + 2 + 2i Reorder the terms: 2i + 2ix + 3x = x + 2 + 2i Reorder the terms: 2i + 2ix + 3x = 2 + 2i + x Add '-2i' to each side of the equation. 2i + 2ix + -2i + 3x = 2 + 2i + -2i + x Reorder the terms: 2i + -2i + 2ix + 3x = 2 + 2i + -2i + x Combine like terms: 2i + -2i = 0 0 + 2ix + 3x = 2 + 2i + -2i + x 2ix + 3x = 2 + 2i + -2i + x Combine like terms: 2i + -2i = 0 2ix + 3x = 2 + 0 + x 2ix + 3x = 2 + x Solving 2ix + 3x = 2 + x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3x' to each side of the equation. 2ix + 3x + -3x = 2 + x + -3x Combine like terms: 3x + -3x = 0 2ix + 0 = 2 + x + -3x 2ix = 2 + x + -3x Combine like terms: x + -3x = -2x 2ix = 2 + -2x Divide each side by '2x'. i = x-1 + -1 Simplifying i = x-1 + -1 Reorder the terms: i = -1 + x-1
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