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