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Simplifying 2Inx = In(6x + -8) Reorder the terms: 2nxI = nI(-8 + 6x) 2nxI = (-8 * nI + 6x * nI) 2nxI = (-8nI + 6nxI) Solving 2nxI = -8nI + 6nxI 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. 8nI + 2nxI = -8nI + 8nI + 6nxI Combine like terms: -8nI + 8nI = 0 8nI + 2nxI = 0 + 6nxI 8nI + 2nxI = 6nxI Add '-6nxI' to each side of the equation. 8nI + 2nxI + -6nxI = 6nxI + -6nxI Combine like terms: 2nxI + -6nxI = -4nxI 8nI + -4nxI = 6nxI + -6nxI Combine like terms: 6nxI + -6nxI = 0 8nI + -4nxI = 0 Factor out the Greatest Common Factor (GCF), '4nI'. 4nI(2 + -1x) = 0 Ignore the factor 4.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 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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