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Simplifying (1 + -2i) * x + 6x + -1ix = (2 + 3i) * x + 5 + -6i Reorder the terms for easier multiplication: x(1 + -2i) + 6x + -1ix = (2 + 3i) * x + 5 + -6i (1 * x + -2i * x) + 6x + -1ix = (2 + 3i) * x + 5 + -6i Reorder the terms: (-2ix + 1x) + 6x + -1ix = (2 + 3i) * x + 5 + -6i (-2ix + 1x) + 6x + -1ix = (2 + 3i) * x + 5 + -6i Reorder the terms: -2ix + -1ix + 1x + 6x = (2 + 3i) * x + 5 + -6i Combine like terms: -2ix + -1ix = -3ix -3ix + 1x + 6x = (2 + 3i) * x + 5 + -6i Combine like terms: 1x + 6x = 7x -3ix + 7x = (2 + 3i) * x + 5 + -6i Reorder the terms for easier multiplication: -3ix + 7x = x(2 + 3i) + 5 + -6i -3ix + 7x = (2 * x + 3i * x) + 5 + -6i Reorder the terms: -3ix + 7x = (3ix + 2x) + 5 + -6i -3ix + 7x = (3ix + 2x) + 5 + -6i Reorder the terms: -3ix + 7x = 5 + -6i + 3ix + 2x Solving -3ix + 7x = 5 + -6i + 3ix + 2x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6i' to each side of the equation. -3ix + 6i + 7x = 5 + -6i + 3ix + 6i + 2x Reorder the terms: 6i + -3ix + 7x = 5 + -6i + 3ix + 6i + 2x Reorder the terms: 6i + -3ix + 7x = 5 + -6i + 6i + 3ix + 2x Combine like terms: -6i + 6i = 0 6i + -3ix + 7x = 5 + 0 + 3ix + 2x 6i + -3ix + 7x = 5 + 3ix + 2x Add '-3ix' to each side of the equation. 6i + -3ix + -3ix + 7x = 5 + 3ix + -3ix + 2x Combine like terms: -3ix + -3ix = -6ix 6i + -6ix + 7x = 5 + 3ix + -3ix + 2x Combine like terms: 3ix + -3ix = 0 6i + -6ix + 7x = 5 + 0 + 2x 6i + -6ix + 7x = 5 + 2x Add '-7x' to each side of the equation. 6i + -6ix + 7x + -7x = 5 + 2x + -7x Combine like terms: 7x + -7x = 0 6i + -6ix + 0 = 5 + 2x + -7x 6i + -6ix = 5 + 2x + -7x Combine like terms: 2x + -7x = -5x 6i + -6ix = 5 + -5x Reorder the terms: -5 + 6i + -6ix + 5x = 5 + -5x + -5 + 5x Reorder the terms: -5 + 6i + -6ix + 5x = 5 + -5 + -5x + 5x Combine like terms: 5 + -5 = 0 -5 + 6i + -6ix + 5x = 0 + -5x + 5x -5 + 6i + -6ix + 5x = -5x + 5x Combine like terms: -5x + 5x = 0 -5 + 6i + -6ix + 5x = 0 The solution to this equation could not be determined.
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