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Simplifying 3x + -15i = -21 + 3yi Reorder the terms: -15i + 3x = -21 + 3yi Solving -15i + 3x = -21 + 3iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3iy' to each side of the equation. -15i + -3iy + 3x = -21 + 3iy + -3iy Combine like terms: 3iy + -3iy = 0 -15i + -3iy + 3x = -21 + 0 -15i + -3iy + 3x = -21 Add '-3x' to each side of the equation. -15i + -3iy + 3x + -3x = -21 + -3x Combine like terms: 3x + -3x = 0 -15i + -3iy + 0 = -21 + -3x -15i + -3iy = -21 + -3x Reorder the terms: 21 + -15i + -3iy + 3x = -21 + -3x + 21 + 3x Reorder the terms: 21 + -15i + -3iy + 3x = -21 + 21 + -3x + 3x Combine like terms: -21 + 21 = 0 21 + -15i + -3iy + 3x = 0 + -3x + 3x 21 + -15i + -3iy + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 21 + -15i + -3iy + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -5i + -1iy + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -5i + -1iy + x)' equal to zero and attempt to solve: Simplifying 7 + -5i + -1iy + x = 0 Solving 7 + -5i + -1iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -5i + -1iy + -7 + x = 0 + -7 Reorder the terms: 7 + -7 + -5i + -1iy + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5i + -1iy + x = 0 + -7 -5i + -1iy + x = 0 + -7 Combine like terms: 0 + -7 = -7 -5i + -1iy + x = -7 Add '-1x' to each side of the equation. -5i + -1iy + x + -1x = -7 + -1x Combine like terms: x + -1x = 0 -5i + -1iy + 0 = -7 + -1x -5i + -1iy = -7 + -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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