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Simplifying 5x + 3i(x + 1) = (1 + i) * x + 7i Reorder the terms: 5x + 3i(1 + x) = (1 + i) * x + 7i 5x + (1 * 3i + x * 3i) = (1 + i) * x + 7i 5x + (3i + 3ix) = (1 + i) * x + 7i Reorder the terms: 3i + 3ix + 5x = (1 + i) * x + 7i Reorder the terms for easier multiplication: 3i + 3ix + 5x = x(1 + i) + 7i 3i + 3ix + 5x = (1 * x + i * x) + 7i Reorder the terms: 3i + 3ix + 5x = (ix + 1x) + 7i 3i + 3ix + 5x = (ix + 1x) + 7i Reorder the terms: 3i + 3ix + 5x = 7i + ix + 1x Solving 3i + 3ix + 5x = 7i + ix + 1x 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. 3i + 3ix + -7i + 5x = 7i + ix + -7i + 1x Reorder the terms: 3i + -7i + 3ix + 5x = 7i + ix + -7i + 1x Combine like terms: 3i + -7i = -4i -4i + 3ix + 5x = 7i + ix + -7i + 1x Reorder the terms: -4i + 3ix + 5x = 7i + -7i + ix + 1x Combine like terms: 7i + -7i = 0 -4i + 3ix + 5x = 0 + ix + 1x -4i + 3ix + 5x = ix + 1x Add '-1ix' to each side of the equation. -4i + 3ix + -1ix + 5x = ix + -1ix + 1x Combine like terms: 3ix + -1ix = 2ix -4i + 2ix + 5x = ix + -1ix + 1x Combine like terms: ix + -1ix = 0 -4i + 2ix + 5x = 0 + 1x -4i + 2ix + 5x = 1x Add '-5x' to each side of the equation. -4i + 2ix + 5x + -5x = 1x + -5x Combine like terms: 5x + -5x = 0 -4i + 2ix + 0 = 1x + -5x -4i + 2ix = 1x + -5x Combine like terms: 1x + -5x = -4x -4i + 2ix = -4x Combine like terms: -4x + 4x = 0 -4i + 2ix + 4x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2i + ix + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2i + ix + 2x)' equal to zero and attempt to solve: Simplifying -2i + ix + 2x = 0 Solving -2i + ix + 2x = 0 Move all terms containing i to the left, all other terms to the right. Add '-2x' to each side of the equation. -2i + ix + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 -2i + ix + 0 = 0 + -2x -2i + ix = 0 + -2x Remove the zero: -2i + ix = -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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