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Simplifying ln(-6y + 7) + -1ln(y + 4) = ln(-11y + -6) Reorder the terms: ln(7 + -6y) + -1ln(y + 4) = ln(-11y + -6) (7 * ln + -6y * ln) + -1ln(y + 4) = ln(-11y + -6) (7ln + -6lny) + -1ln(y + 4) = ln(-11y + -6) Reorder the terms: 7ln + -6lny + -1ln(4 + y) = ln(-11y + -6) 7ln + -6lny + (4 * -1ln + y * -1ln) = ln(-11y + -6) 7ln + -6lny + (-4ln + -1lny) = ln(-11y + -6) Reorder the terms: 7ln + -4ln + -6lny + -1lny = ln(-11y + -6) Combine like terms: 7ln + -4ln = 3ln 3ln + -6lny + -1lny = ln(-11y + -6) Combine like terms: -6lny + -1lny = -7lny 3ln + -7lny = ln(-11y + -6) Reorder the terms: 3ln + -7lny = ln(-6 + -11y) 3ln + -7lny = (-6 * ln + -11y * ln) 3ln + -7lny = (-6ln + -11lny) Solving 3ln + -7lny = -6ln + -11lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 3ln + 6ln + -7lny = -6ln + 6ln + -11lny Combine like terms: 3ln + 6ln = 9ln 9ln + -7lny = -6ln + 6ln + -11lny Combine like terms: -6ln + 6ln = 0 9ln + -7lny = 0 + -11lny 9ln + -7lny = -11lny Add '11lny' to each side of the equation. 9ln + -7lny + 11lny = -11lny + 11lny Combine like terms: -7lny + 11lny = 4lny 9ln + 4lny = -11lny + 11lny Combine like terms: -11lny + 11lny = 0 9ln + 4lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 4y) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(9 + 4y)' equal to zero and attempt to solve: Simplifying 9 + 4y = 0 Solving 9 + 4y = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4y = 0 + -9 4y = 0 + -9 Combine like terms: 0 + -9 = -9 4y = -9 Add '-4y' to each side of the equation. 4y + -4y = -9 + -4y Combine like terms: 4y + -4y = 0 0 = -9 + -4y Simplifying 0 = -9 + -4y 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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