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Simplifying 3x + 4i = 15 + -3yi + i Reorder the terms: 4i + 3x = 15 + -3yi + i Reorder the terms: 4i + 3x = 15 + i + -3iy Solving 4i + 3x = 15 + i + -3iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. 4i + -1i + 3x = 15 + i + -1i + -3iy Combine like terms: 4i + -1i = 3i 3i + 3x = 15 + i + -1i + -3iy Combine like terms: i + -1i = 0 3i + 3x = 15 + 0 + -3iy 3i + 3x = 15 + -3iy Add '3iy' to each side of the equation. 3i + 3iy + 3x = 15 + -3iy + 3iy Combine like terms: -3iy + 3iy = 0 3i + 3iy + 3x = 15 + 0 3i + 3iy + 3x = 15 Add '-3x' to each side of the equation. 3i + 3iy + 3x + -3x = 15 + -3x Combine like terms: 3x + -3x = 0 3i + 3iy + 0 = 15 + -3x 3i + 3iy = 15 + -3x Reorder the terms: -15 + 3i + 3iy + 3x = 15 + -3x + -15 + 3x Reorder the terms: -15 + 3i + 3iy + 3x = 15 + -15 + -3x + 3x Combine like terms: 15 + -15 = 0 -15 + 3i + 3iy + 3x = 0 + -3x + 3x -15 + 3i + 3iy + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 -15 + 3i + 3iy + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + i + iy + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + i + iy + x)' equal to zero and attempt to solve: Simplifying -5 + i + iy + x = 0 Solving -5 + i + iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + i + iy + 5 + x = 0 + 5 Reorder the terms: -5 + 5 + i + iy + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + i + iy + x = 0 + 5 i + iy + x = 0 + 5 Combine like terms: 0 + 5 = 5 i + iy + x = 5 Add '-1x' to each side of the equation. i + iy + x + -1x = 5 + -1x Combine like terms: x + -1x = 0 i + iy + 0 = 5 + -1x i + iy = 5 + -1x 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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