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Simplifying In(x + 6) + In(x) = In(x + 36) Reorder the terms: nI(6 + x) + In(x) = In(x + 36) (6 * nI + x * nI) + In(x) = In(x + 36) (6nI + nxI) + In(x) = In(x + 36) Multiply nI * x 6nI + nxI + nxI = In(x + 36) Combine like terms: nxI + nxI = 2nxI 6nI + 2nxI = In(x + 36) Reorder the terms: 6nI + 2nxI = nI(36 + x) 6nI + 2nxI = (36 * nI + x * nI) 6nI + 2nxI = (36nI + nxI) Solving 6nI + 2nxI = 36nI + nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-36nI' to each side of the equation. 6nI + -36nI + 2nxI = 36nI + -36nI + nxI Combine like terms: 6nI + -36nI = -30nI -30nI + 2nxI = 36nI + -36nI + nxI Combine like terms: 36nI + -36nI = 0 -30nI + 2nxI = 0 + nxI -30nI + 2nxI = nxI Add '-1nxI' to each side of the equation. -30nI + 2nxI + -1nxI = nxI + -1nxI Combine like terms: 2nxI + -1nxI = 1nxI -30nI + 1nxI = nxI + -1nxI Combine like terms: nxI + -1nxI = 0 -30nI + 1nxI = 0 Factor out the Greatest Common Factor (GCF), 'nI'. nI(-30 + x) = 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 '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Add '-1x' to each side of the equation. x + -1x = 30 + -1x Combine like terms: x + -1x = 0 0 = 30 + -1x Simplifying 0 = 30 + -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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