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Simplifying Ln(-4y + 2) + -1ln(y + 7) = ln(-9y + -12) Reorder the terms: nL(2 + -4y) + -1ln(y + 7) = ln(-9y + -12) (2 * nL + -4y * nL) + -1ln(y + 7) = ln(-9y + -12) (2nL + -4nyL) + -1ln(y + 7) = ln(-9y + -12) Reorder the terms: 2nL + -4nyL + -1ln(7 + y) = ln(-9y + -12) 2nL + -4nyL + (7 * -1ln + y * -1ln) = ln(-9y + -12) 2nL + -4nyL + (-7ln + -1lny) = ln(-9y + -12) Reorder the terms: -7ln + -1lny + 2nL + -4nyL = ln(-9y + -12) Reorder the terms: -7ln + -1lny + 2nL + -4nyL = ln(-12 + -9y) -7ln + -1lny + 2nL + -4nyL = (-12 * ln + -9y * ln) -7ln + -1lny + 2nL + -4nyL = (-12ln + -9lny) Solving -7ln + -1lny + 2nL + -4nyL = -12ln + -9lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. -7ln + -1lny + 2nL + 12ln + -4nyL = -12ln + 12ln + -9lny Reorder the terms: -7ln + 12ln + -1lny + 2nL + -4nyL = -12ln + 12ln + -9lny Combine like terms: -7ln + 12ln = 5ln 5ln + -1lny + 2nL + -4nyL = -12ln + 12ln + -9lny Combine like terms: -12ln + 12ln = 0 5ln + -1lny + 2nL + -4nyL = 0 + -9lny 5ln + -1lny + 2nL + -4nyL = -9lny Add '9lny' to each side of the equation. 5ln + -1lny + 2nL + 9lny + -4nyL = -9lny + 9lny Reorder the terms: 5ln + -1lny + 9lny + 2nL + -4nyL = -9lny + 9lny Combine like terms: -1lny + 9lny = 8lny 5ln + 8lny + 2nL + -4nyL = -9lny + 9lny Combine like terms: -9lny + 9lny = 0 5ln + 8lny + 2nL + -4nyL = 0 Add '-2nL' to each side of the equation. 5ln + 8lny + 2nL + -2nL + -4nyL = 0 + -2nL Combine like terms: 2nL + -2nL = 0 5ln + 8lny + 0 + -4nyL = 0 + -2nL 5ln + 8lny + -4nyL = 0 + -2nL Remove the zero: 5ln + 8lny + -4nyL = -2nL Add '4nyL' to each side of the equation. 5ln + 8lny + -4nyL + 4nyL = -2nL + 4nyL Combine like terms: -4nyL + 4nyL = 0 5ln + 8lny + 0 = -2nL + 4nyL 5ln + 8lny = -2nL + 4nyL Reorder the terms: 5ln + 8lny + 2nL + -4nyL = -2nL + 2nL + 4nyL + -4nyL Combine like terms: -2nL + 2nL = 0 5ln + 8lny + 2nL + -4nyL = 0 + 4nyL + -4nyL 5ln + 8lny + 2nL + -4nyL = 4nyL + -4nyL Combine like terms: 4nyL + -4nyL = 0 5ln + 8lny + 2nL + -4nyL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(5l + 8ly + 2L + -4yL) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(5l + 8ly + 2L + -4yL)' equal to zero and attempt to solve: Simplifying 5l + 8ly + 2L + -4yL = 0 Reorder the terms: 2L + 5l + 8ly + -4yL = 0 Solving 2L + 5l + 8ly + -4yL = 0 Move all terms containing l to the left, all other terms to the right. Add '-2L' to each side of the equation. 2L + 5l + 8ly + -2L + -4yL = 0 + -2L Reorder the terms: 2L + -2L + 5l + 8ly + -4yL = 0 + -2L Combine like terms: 2L + -2L = 0 0 + 5l + 8ly + -4yL = 0 + -2L 5l + 8ly + -4yL = 0 + -2L Remove the zero: 5l + 8ly + -4yL = -2L Add '4yL' to each side of the equation. 5l + 8ly + -4yL + 4yL = -2L + 4yL Combine like terms: -4yL + 4yL = 0 5l + 8ly + 0 = -2L + 4yL 5l + 8ly = -2L + 4yL 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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