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Simplifying In(10 + -1x) + In(-6 + -1x) = In(-34 + -15x) (10 * nI + -1x * nI) + In(-6 + -1x) = In(-34 + -15x) (10nI + -1nxI) + In(-6 + -1x) = In(-34 + -15x) 10nI + -1nxI + (-6 * nI + -1x * nI) = In(-34 + -15x) 10nI + -1nxI + (-6nI + -1nxI) = In(-34 + -15x) Reorder the terms: 10nI + -6nI + -1nxI + -1nxI = In(-34 + -15x) Combine like terms: 10nI + -6nI = 4nI 4nI + -1nxI + -1nxI = In(-34 + -15x) Combine like terms: -1nxI + -1nxI = -2nxI 4nI + -2nxI = In(-34 + -15x) 4nI + -2nxI = (-34 * nI + -15x * nI) 4nI + -2nxI = (-34nI + -15nxI) Solving 4nI + -2nxI = -34nI + -15nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '34nI' to each side of the equation. 4nI + 34nI + -2nxI = -34nI + 34nI + -15nxI Combine like terms: 4nI + 34nI = 38nI 38nI + -2nxI = -34nI + 34nI + -15nxI Combine like terms: -34nI + 34nI = 0 38nI + -2nxI = 0 + -15nxI 38nI + -2nxI = -15nxI Add '15nxI' to each side of the equation. 38nI + -2nxI + 15nxI = -15nxI + 15nxI Combine like terms: -2nxI + 15nxI = 13nxI 38nI + 13nxI = -15nxI + 15nxI Combine like terms: -15nxI + 15nxI = 0 38nI + 13nxI = 0 Factor out the Greatest Common Factor (GCF), 'nI'. nI(38 + 13x) = 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 '(38 + 13x)' equal to zero and attempt to solve: Simplifying 38 + 13x = 0 Solving 38 + 13x = 0 Move all terms containing n to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + 13x = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 13x = 0 + -38 13x = 0 + -38 Combine like terms: 0 + -38 = -38 13x = -38 Add '-13x' to each side of the equation. 13x + -13x = -38 + -13x Combine like terms: 13x + -13x = 0 0 = -38 + -13x Simplifying 0 = -38 + -13x 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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