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Simplifying In(5x + 11) = In(3x + 3) Reorder the terms: nI(11 + 5x) = In(3x + 3) (11 * nI + 5x * nI) = In(3x + 3) (11nI + 5nxI) = In(3x + 3) Reorder the terms: 11nI + 5nxI = nI(3 + 3x) 11nI + 5nxI = (3 * nI + 3x * nI) 11nI + 5nxI = (3nI + 3nxI) Solving 11nI + 5nxI = 3nI + 3nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3nI' to each side of the equation. 11nI + -3nI + 5nxI = 3nI + -3nI + 3nxI Combine like terms: 11nI + -3nI = 8nI 8nI + 5nxI = 3nI + -3nI + 3nxI Combine like terms: 3nI + -3nI = 0 8nI + 5nxI = 0 + 3nxI 8nI + 5nxI = 3nxI Add '-3nxI' to each side of the equation. 8nI + 5nxI + -3nxI = 3nxI + -3nxI Combine like terms: 5nxI + -3nxI = 2nxI 8nI + 2nxI = 3nxI + -3nxI Combine like terms: 3nxI + -3nxI = 0 8nI + 2nxI = 0 Factor out the Greatest Common Factor (GCF), '2nI'. 2nI(4 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'nI' equal to zero and attempt to solve: Simplifying nI = 0 Solving nI = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nI = 0 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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