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Simplifying In(7x + 40) = In(2x + 5) Reorder the terms: nI(40 + 7x) = In(2x + 5) (40 * nI + 7x * nI) = In(2x + 5) (40nI + 7nxI) = In(2x + 5) Reorder the terms: 40nI + 7nxI = nI(5 + 2x) 40nI + 7nxI = (5 * nI + 2x * nI) 40nI + 7nxI = (5nI + 2nxI) Solving 40nI + 7nxI = 5nI + 2nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5nI' to each side of the equation. 40nI + -5nI + 7nxI = 5nI + -5nI + 2nxI Combine like terms: 40nI + -5nI = 35nI 35nI + 7nxI = 5nI + -5nI + 2nxI Combine like terms: 5nI + -5nI = 0 35nI + 7nxI = 0 + 2nxI 35nI + 7nxI = 2nxI Add '-2nxI' to each side of the equation. 35nI + 7nxI + -2nxI = 2nxI + -2nxI Combine like terms: 7nxI + -2nxI = 5nxI 35nI + 5nxI = 2nxI + -2nxI Combine like terms: 2nxI + -2nxI = 0 35nI + 5nxI = 0 Factor out the Greatest Common Factor (GCF), '5nI'. 5nI(7 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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