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Simplifying In(7x + 8) = In(2x + -22) Reorder the terms: nI(8 + 7x) = In(2x + -22) (8 * nI + 7x * nI) = In(2x + -22) (8nI + 7nxI) = In(2x + -22) Reorder the terms: 8nI + 7nxI = nI(-22 + 2x) 8nI + 7nxI = (-22 * nI + 2x * nI) 8nI + 7nxI = (-22nI + 2nxI) Solving 8nI + 7nxI = -22nI + 2nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '22nI' to each side of the equation. 8nI + 22nI + 7nxI = -22nI + 22nI + 2nxI Combine like terms: 8nI + 22nI = 30nI 30nI + 7nxI = -22nI + 22nI + 2nxI Combine like terms: -22nI + 22nI = 0 30nI + 7nxI = 0 + 2nxI 30nI + 7nxI = 2nxI Add '-2nxI' to each side of the equation. 30nI + 7nxI + -2nxI = 2nxI + -2nxI Combine like terms: 7nxI + -2nxI = 5nxI 30nI + 5nxI = 2nxI + -2nxI Combine like terms: 2nxI + -2nxI = 0 30nI + 5nxI = 0 Factor out the Greatest Common Factor (GCF), '5nI'. 5nI(6 + x) = 0 Ignore the factor 5.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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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