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Simplifying In(12x + 9) = In(2x + 8) Reorder the terms: nI(9 + 12x) = In(2x + 8) (9 * nI + 12x * nI) = In(2x + 8) (9nI + 12nxI) = In(2x + 8) Reorder the terms: 9nI + 12nxI = nI(8 + 2x) 9nI + 12nxI = (8 * nI + 2x * nI) 9nI + 12nxI = (8nI + 2nxI) Solving 9nI + 12nxI = 8nI + 2nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8nI' to each side of the equation. 9nI + -8nI + 12nxI = 8nI + -8nI + 2nxI Combine like terms: 9nI + -8nI = 1nI 1nI + 12nxI = 8nI + -8nI + 2nxI Combine like terms: 8nI + -8nI = 0 1nI + 12nxI = 0 + 2nxI 1nI + 12nxI = 2nxI Add '-2nxI' to each side of the equation. 1nI + 12nxI + -2nxI = 2nxI + -2nxI Combine like terms: 12nxI + -2nxI = 10nxI 1nI + 10nxI = 2nxI + -2nxI Combine like terms: 2nxI + -2nxI = 0 1nI + 10nxI = 0 Factor out the Greatest Common Factor (GCF), 'nI'. nI(1 + 10x) = 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 + 10x)' equal to zero and attempt to solve: Simplifying 1 + 10x = 0 Solving 1 + 10x = 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 + 10x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10x = 0 + -1 10x = 0 + -1 Combine like terms: 0 + -1 = -1 10x = -1 Add '-10x' to each side of the equation. 10x + -10x = -1 + -10x Combine like terms: 10x + -10x = 0 0 = -1 + -10x Simplifying 0 = -1 + -10x 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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