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