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Simplifying In(x + 4) + -1In(x + 6) = In(x + 3) Reorder the terms: nI(4 + x) + -1In(x + 6) = In(x + 3) (4 * nI + x * nI) + -1In(x + 6) = In(x + 3) (4nI + nxI) + -1In(x + 6) = In(x + 3) Reorder the terms: 4nI + nxI + -1nI(6 + x) = In(x + 3) 4nI + nxI + (6 * -1nI + x * -1nI) = In(x + 3) 4nI + nxI + (-6nI + -1nxI) = In(x + 3) Reorder the terms: 4nI + -6nI + nxI + -1nxI = In(x + 3) Combine like terms: 4nI + -6nI = -2nI -2nI + nxI + -1nxI = In(x + 3) Combine like terms: nxI + -1nxI = 0 -2nI + 0 = In(x + 3) -2nI = In(x + 3) Reorder the terms: -2nI = nI(3 + x) -2nI = (3 * nI + x * nI) -2nI = (3nI + nxI) Solving -2nI = 3nI + nxI 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. -2nI + -3nI = 3nI + -3nI + nxI Combine like terms: -2nI + -3nI = -5nI -5nI = 3nI + -3nI + nxI Combine like terms: 3nI + -3nI = 0 -5nI = 0 + nxI -5nI = nxI Add '-1nxI' to each side of the equation. -5nI + -1nxI = nxI + -1nxI Combine like terms: nxI + -1nxI = 0 -5nI + -1nxI = 0 Factor out the Greatest Common Factor (GCF), '-1nI'. -1nI(5 + x) = 0 Ignore the factor -1.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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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