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Simplifying In(5 + -1x) + in(-3 + -1x) = in(1 + -8x) (5 * nI + -1x * nI) + in(-3 + -1x) = in(1 + -8x) (5nI + -1nxI) + in(-3 + -1x) = in(1 + -8x) 5nI + -1nxI + (-3 * in + -1x * in) = in(1 + -8x) 5nI + -1nxI + (-3in + -1inx) = in(1 + -8x) Reorder the terms: -3in + -1inx + 5nI + -1nxI = in(1 + -8x) -3in + -1inx + 5nI + -1nxI = (1 * in + -8x * in) -3in + -1inx + 5nI + -1nxI = (1in + -8inx) Solving -3in + -1inx + 5nI + -1nxI = 1in + -8inx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1in' to each side of the equation. -3in + -1inx + 5nI + -1in + -1nxI = 1in + -1in + -8inx Reorder the terms: -3in + -1in + -1inx + 5nI + -1nxI = 1in + -1in + -8inx Combine like terms: -3in + -1in = -4in -4in + -1inx + 5nI + -1nxI = 1in + -1in + -8inx Combine like terms: 1in + -1in = 0 -4in + -1inx + 5nI + -1nxI = 0 + -8inx -4in + -1inx + 5nI + -1nxI = -8inx Add '8inx' to each side of the equation. -4in + -1inx + 5nI + 8inx + -1nxI = -8inx + 8inx Reorder the terms: -4in + -1inx + 8inx + 5nI + -1nxI = -8inx + 8inx Combine like terms: -1inx + 8inx = 7inx -4in + 7inx + 5nI + -1nxI = -8inx + 8inx Combine like terms: -8inx + 8inx = 0 -4in + 7inx + 5nI + -1nxI = 0 Add '-5nI' to each side of the equation. -4in + 7inx + 5nI + -5nI + -1nxI = 0 + -5nI Combine like terms: 5nI + -5nI = 0 -4in + 7inx + 0 + -1nxI = 0 + -5nI -4in + 7inx + -1nxI = 0 + -5nI Remove the zero: -4in + 7inx + -1nxI = -5nI Add 'nxI' to each side of the equation. -4in + 7inx + -1nxI + nxI = -5nI + nxI Combine like terms: -1nxI + nxI = 0 -4in + 7inx + 0 = -5nI + nxI -4in + 7inx = -5nI + nxI Reorder the terms: -4in + 7inx + 5nI + -1nxI = -5nI + 5nI + nxI + -1nxI Combine like terms: -5nI + 5nI = 0 -4in + 7inx + 5nI + -1nxI = 0 + nxI + -1nxI -4in + 7inx + 5nI + -1nxI = nxI + -1nxI Combine like terms: nxI + -1nxI = 0 -4in + 7inx + 5nI + -1nxI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-4i + 7ix + 5I + -1xI) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing i to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4i + 7ix + 5I + -1xI)' equal to zero and attempt to solve: Simplifying -4i + 7ix + 5I + -1xI = 0 Reorder the terms: 5I + -4i + 7ix + -1xI = 0 Solving 5I + -4i + 7ix + -1xI = 0 Move all terms containing i to the left, all other terms to the right. Add '-5I' to each side of the equation. 5I + -4i + 7ix + -5I + -1xI = 0 + -5I Reorder the terms: 5I + -5I + -4i + 7ix + -1xI = 0 + -5I Combine like terms: 5I + -5I = 0 0 + -4i + 7ix + -1xI = 0 + -5I -4i + 7ix + -1xI = 0 + -5I Remove the zero: -4i + 7ix + -1xI = -5I Add 'xI' to each side of the equation. -4i + 7ix + -1xI + xI = -5I + xI Combine like terms: -1xI + xI = 0 -4i + 7ix + 0 = -5I + xI -4i + 7ix = -5I + xI 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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