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