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Simplifying (3x + y) + -1(2x + 5y) * i = 4 + -7i Remove parenthesis around (3x + y) 3x + y + -1(2x + 5y) * i = 4 + -7i Reorder the terms for easier multiplication: 3x + y + -1i(2x + 5y) = 4 + -7i 3x + y + (2x * -1i + 5y * -1i) = 4 + -7i 3x + y + (-2ix + -5iy) = 4 + -7i Reorder the terms: -2ix + -5iy + 3x + y = 4 + -7i Solving -2ix + -5iy + 3x + y = 4 + -7i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '7i' to each side of the equation. -2ix + -5iy + 3x + 7i + y = 4 + -7i + 7i Reorder the terms: 7i + -2ix + -5iy + 3x + y = 4 + -7i + 7i Combine like terms: -7i + 7i = 0 7i + -2ix + -5iy + 3x + y = 4 + 0 7i + -2ix + -5iy + 3x + y = 4 Add '-3x' to each side of the equation. 7i + -2ix + -5iy + 3x + -3x + y = 4 + -3x Combine like terms: 3x + -3x = 0 7i + -2ix + -5iy + 0 + y = 4 + -3x 7i + -2ix + -5iy + y = 4 + -3x Add '-1y' to each side of the equation. 7i + -2ix + -5iy + y + -1y = 4 + -3x + -1y Combine like terms: y + -1y = 0 7i + -2ix + -5iy + 0 = 4 + -3x + -1y 7i + -2ix + -5iy = 4 + -3x + -1y Reorder the terms: -4 + 7i + -2ix + -5iy + 3x + y = 4 + -3x + -1y + -4 + 3x + y Reorder the terms: -4 + 7i + -2ix + -5iy + 3x + y = 4 + -4 + -3x + 3x + -1y + y Combine like terms: 4 + -4 = 0 -4 + 7i + -2ix + -5iy + 3x + y = 0 + -3x + 3x + -1y + y -4 + 7i + -2ix + -5iy + 3x + y = -3x + 3x + -1y + y Combine like terms: -3x + 3x = 0 -4 + 7i + -2ix + -5iy + 3x + y = 0 + -1y + y -4 + 7i + -2ix + -5iy + 3x + y = -1y + y Combine like terms: -1y + y = 0 -4 + 7i + -2ix + -5iy + 3x + y = 0 The solution to this equation could not be determined.
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