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Simplifying in(3x + -4) + in(x + 2) = In(2x + 1) + In(x + 2) Reorder the terms: in(-4 + 3x) + in(x + 2) = In(2x + 1) + In(x + 2) (-4 * in + 3x * in) + in(x + 2) = In(2x + 1) + In(x + 2) (-4in + 3inx) + in(x + 2) = In(2x + 1) + In(x + 2) Reorder the terms: -4in + 3inx + in(2 + x) = In(2x + 1) + In(x + 2) -4in + 3inx + (2 * in + x * in) = In(2x + 1) + In(x + 2) -4in + 3inx + (2in + inx) = In(2x + 1) + In(x + 2) Reorder the terms: -4in + 2in + 3inx + inx = In(2x + 1) + In(x + 2) Combine like terms: -4in + 2in = -2in -2in + 3inx + inx = In(2x + 1) + In(x + 2) Combine like terms: 3inx + inx = 4inx -2in + 4inx = In(2x + 1) + In(x + 2) Reorder the terms: -2in + 4inx = nI(1 + 2x) + In(x + 2) -2in + 4inx = (1 * nI + 2x * nI) + In(x + 2) -2in + 4inx = (1nI + 2nxI) + In(x + 2) Reorder the terms: -2in + 4inx = 1nI + 2nxI + nI(2 + x) -2in + 4inx = 1nI + 2nxI + (2 * nI + x * nI) -2in + 4inx = 1nI + 2nxI + (2nI + nxI) Reorder the terms: -2in + 4inx = 1nI + 2nI + 2nxI + nxI Combine like terms: 1nI + 2nI = 3nI -2in + 4inx = 3nI + 2nxI + nxI Combine like terms: 2nxI + nxI = 3nxI -2in + 4inx = 3nI + 3nxI Solving -2in + 4inx = 3nI + 3nxI Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: -2in + 4inx + -3nI + -3nxI = 3nI + -3nI + 3nxI + -3nxI Combine like terms: 3nI + -3nI = 0 -2in + 4inx + -3nI + -3nxI = 0 + 3nxI + -3nxI -2in + 4inx + -3nI + -3nxI = 3nxI + -3nxI Combine like terms: 3nxI + -3nxI = 0 -2in + 4inx + -3nI + -3nxI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-2i + 4ix + -3I + -3xI) = 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 '(-2i + 4ix + -3I + -3xI)' equal to zero and attempt to solve: Simplifying -2i + 4ix + -3I + -3xI = 0 Reorder the terms: -3I + -2i + 4ix + -3xI = 0 Solving -3I + -2i + 4ix + -3xI = 0 Move all terms containing i to the left, all other terms to the right. Add '3I' to each side of the equation. -3I + -2i + 4ix + 3I + -3xI = 0 + 3I Reorder the terms: -3I + 3I + -2i + 4ix + -3xI = 0 + 3I Combine like terms: -3I + 3I = 0 0 + -2i + 4ix + -3xI = 0 + 3I -2i + 4ix + -3xI = 0 + 3I Remove the zero: -2i + 4ix + -3xI = 3I Add '3xI' to each side of the equation. -2i + 4ix + -3xI + 3xI = 3I + 3xI Combine like terms: -3xI + 3xI = 0 -2i + 4ix + 0 = 3I + 3xI -2i + 4ix = 3I + 3xI 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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