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Simplifying 3x + i(x + 1) = x + 2 + 2i Reorder the terms: 3x + i(1 + x) = x + 2 + 2i 3x + (1 * i + x * i) = x + 2 + 2i 3x + (1i + ix) = x + 2 + 2i Reorder the terms: 1i + ix + 3x = x + 2 + 2i Reorder the terms: 1i + ix + 3x = 2 + 2i + x Solving 1i + ix + 3x = 2 + 2i + x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2i' to each side of the equation. 1i + ix + -2i + 3x = 2 + 2i + -2i + x Reorder the terms: 1i + -2i + ix + 3x = 2 + 2i + -2i + x Combine like terms: 1i + -2i = -1i -1i + ix + 3x = 2 + 2i + -2i + x Combine like terms: 2i + -2i = 0 -1i + ix + 3x = 2 + 0 + x -1i + ix + 3x = 2 + x Add '-3x' to each side of the equation. -1i + ix + 3x + -3x = 2 + x + -3x Combine like terms: 3x + -3x = 0 -1i + ix + 0 = 2 + x + -3x -1i + ix = 2 + x + -3x Combine like terms: x + -3x = -2x -1i + ix = 2 + -2x Reorder the terms: -2 + -1i + ix + 2x = 2 + -2x + -2 + 2x Reorder the terms: -2 + -1i + ix + 2x = 2 + -2 + -2x + 2x Combine like terms: 2 + -2 = 0 -2 + -1i + ix + 2x = 0 + -2x + 2x -2 + -1i + ix + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 -2 + -1i + ix + 2x = 0 The solution to this equation could not be determined.
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