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Simplifying In(x + 3) + In(x + 8) = In(14) Reorder the terms: nI(3 + x) + In(x + 8) = In(14) (3 * nI + x * nI) + In(x + 8) = In(14) (3nI + nxI) + In(x + 8) = In(14) Reorder the terms: 3nI + nxI + nI(8 + x) = In(14) 3nI + nxI + (8 * nI + x * nI) = In(14) 3nI + nxI + (8nI + nxI) = In(14) Reorder the terms: 3nI + 8nI + nxI + nxI = In(14) Combine like terms: 3nI + 8nI = 11nI 11nI + nxI + nxI = In(14) Combine like terms: nxI + nxI = 2nxI 11nI + 2nxI = In(14) Reorder the terms for easier multiplication: 11nI + 2nxI = 14nI Solving 11nI + 2nxI = 14nI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-14nI' to each side of the equation. 11nI + -14nI + 2nxI = 14nI + -14nI Combine like terms: 11nI + -14nI = -3nI -3nI + 2nxI = 14nI + -14nI Combine like terms: 14nI + -14nI = 0 -3nI + 2nxI = 0 Factor out the Greatest Common Factor (GCF), 'nI'. nI(-3 + 2x) = 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -2x 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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