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