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Simplifying 2In(x + -1) + In(4) = In(10 + -3x) Reorder the terms: 2nI(-1 + x) + In(4) = In(10 + -3x) (-1 * 2nI + x * 2nI) + In(4) = In(10 + -3x) (-2nI + 2nxI) + In(4) = In(10 + -3x) Reorder the terms for easier multiplication: -2nI + 2nxI + 4nI = In(10 + -3x) Reorder the terms: -2nI + 4nI + 2nxI = In(10 + -3x) Combine like terms: -2nI + 4nI = 2nI 2nI + 2nxI = In(10 + -3x) 2nI + 2nxI = (10 * nI + -3x * nI) 2nI + 2nxI = (10nI + -3nxI) Solving 2nI + 2nxI = 10nI + -3nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10nI' to each side of the equation. 2nI + -10nI + 2nxI = 10nI + -10nI + -3nxI Combine like terms: 2nI + -10nI = -8nI -8nI + 2nxI = 10nI + -10nI + -3nxI Combine like terms: 10nI + -10nI = 0 -8nI + 2nxI = 0 + -3nxI -8nI + 2nxI = -3nxI Add '3nxI' to each side of the equation. -8nI + 2nxI + 3nxI = -3nxI + 3nxI Combine like terms: 2nxI + 3nxI = 5nxI -8nI + 5nxI = -3nxI + 3nxI Combine like terms: -3nxI + 3nxI = 0 -8nI + 5nxI = 0 Factor out the Greatest Common Factor (GCF), 'nI'. nI(-8 + 5x) = 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 '(-8 + 5x)' equal to zero and attempt to solve: Simplifying -8 + 5x = 0 Solving -8 + 5x = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 5x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5x = 0 + 8 5x = 0 + 8 Combine like terms: 0 + 8 = 8 5x = 8 Add '-5x' to each side of the equation. 5x + -5x = 8 + -5x Combine like terms: 5x + -5x = 0 0 = 8 + -5x Simplifying 0 = 8 + -5x 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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