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Simplifying In(X + -9) = in(5x + 5) Reorder the terms: nI(-9 + X) = in(5x + 5) (-9 * nI + X * nI) = in(5x + 5) (-9nI + nIX) = in(5x + 5) Reorder the terms: -9nI + nIX = in(5 + 5x) -9nI + nIX = (5 * in + 5x * in) -9nI + nIX = (5in + 5inx) Solving -9nI + nIX = 5in + 5inx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5in' to each side of the equation. -9nI + -5in + nIX = 5in + -5in + 5inx Reorder the terms: -5in + -9nI + nIX = 5in + -5in + 5inx Combine like terms: 5in + -5in = 0 -5in + -9nI + nIX = 0 + 5inx -5in + -9nI + nIX = 5inx Add '-5inx' to each side of the equation. -5in + -9nI + -5inx + nIX = 5inx + -5inx Reorder the terms: -5in + -5inx + -9nI + nIX = 5inx + -5inx Combine like terms: 5inx + -5inx = 0 -5in + -5inx + -9nI + nIX = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5i + -5ix + -9I + IX) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-5i + -5ix + -9I + IX)' equal to zero and attempt to solve: Simplifying -5i + -5ix + -9I + IX = 0 Reorder the terms: -9I + IX + -5i + -5ix = 0 Solving -9I + IX + -5i + -5ix = 0 Move all terms containing n to the left, all other terms to the right. Add '9I' to each side of the equation. -9I + IX + -5i + 9I + -5ix = 0 + 9I Reorder the terms: -9I + 9I + IX + -5i + -5ix = 0 + 9I Combine like terms: -9I + 9I = 0 0 + IX + -5i + -5ix = 0 + 9I IX + -5i + -5ix = 0 + 9I Remove the zero: IX + -5i + -5ix = 9I Add '-1IX' to each side of the equation. IX + -5i + -1IX + -5ix = 9I + -1IX Reorder the terms: IX + -1IX + -5i + -5ix = 9I + -1IX Combine like terms: IX + -1IX = 0 0 + -5i + -5ix = 9I + -1IX -5i + -5ix = 9I + -1IX Add '5i' to each side of the equation. -5i + 5i + -5ix = 9I + -1IX + 5i Combine like terms: -5i + 5i = 0 0 + -5ix = 9I + -1IX + 5i -5ix = 9I + -1IX + 5i Add '5ix' to each side of the equation. -5ix + 5ix = 9I + -1IX + 5i + 5ix Combine like terms: -5ix + 5ix = 0 0 = 9I + -1IX + 5i + 5ix Simplifying 0 = 9I + -1IX + 5i + 5ix The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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