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Simplifying Ln(x + -2) + ln(x + 1) = ln(3x + -5) Reorder the terms: nL(-2 + x) + ln(x + 1) = ln(3x + -5) (-2 * nL + x * nL) + ln(x + 1) = ln(3x + -5) (-2nL + nxL) + ln(x + 1) = ln(3x + -5) Reorder the terms: -2nL + nxL + ln(1 + x) = ln(3x + -5) -2nL + nxL + (1 * ln + x * ln) = ln(3x + -5) -2nL + nxL + (1ln + lnx) = ln(3x + -5) Reorder the terms: 1ln + lnx + -2nL + nxL = ln(3x + -5) Reorder the terms: 1ln + lnx + -2nL + nxL = ln(-5 + 3x) 1ln + lnx + -2nL + nxL = (-5 * ln + 3x * ln) 1ln + lnx + -2nL + nxL = (-5ln + 3lnx) Solving 1ln + lnx + -2nL + nxL = -5ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 1ln + lnx + -2nL + 5ln + nxL = -5ln + 5ln + 3lnx Reorder the terms: 1ln + 5ln + lnx + -2nL + nxL = -5ln + 5ln + 3lnx Combine like terms: 1ln + 5ln = 6ln 6ln + lnx + -2nL + nxL = -5ln + 5ln + 3lnx Combine like terms: -5ln + 5ln = 0 6ln + lnx + -2nL + nxL = 0 + 3lnx 6ln + lnx + -2nL + nxL = 3lnx Add '-3lnx' to each side of the equation. 6ln + lnx + -2nL + -3lnx + nxL = 3lnx + -3lnx Reorder the terms: 6ln + lnx + -3lnx + -2nL + nxL = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx 6ln + -2lnx + -2nL + nxL = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 6ln + -2lnx + -2nL + nxL = 0 Add '2nL' to each side of the equation. 6ln + -2lnx + -2nL + 2nL + nxL = 0 + 2nL Combine like terms: -2nL + 2nL = 0 6ln + -2lnx + 0 + nxL = 0 + 2nL 6ln + -2lnx + nxL = 0 + 2nL Remove the zero: 6ln + -2lnx + nxL = 2nL Add '-1nxL' to each side of the equation. 6ln + -2lnx + nxL + -1nxL = 2nL + -1nxL Combine like terms: nxL + -1nxL = 0 6ln + -2lnx + 0 = 2nL + -1nxL 6ln + -2lnx = 2nL + -1nxL Reorder the terms: 6ln + -2lnx + -2nL + nxL = 2nL + -2nL + -1nxL + nxL Combine like terms: 2nL + -2nL = 0 6ln + -2lnx + -2nL + nxL = 0 + -1nxL + nxL 6ln + -2lnx + -2nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 6ln + -2lnx + -2nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(6l + -2lx + -2L + xL) = 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 '(6l + -2lx + -2L + xL)' equal to zero and attempt to solve: Simplifying 6l + -2lx + -2L + xL = 0 Reorder the terms: -2L + 6l + -2lx + xL = 0 Solving -2L + 6l + -2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '2L' to each side of the equation. -2L + 6l + -2lx + 2L + xL = 0 + 2L Reorder the terms: -2L + 2L + 6l + -2lx + xL = 0 + 2L Combine like terms: -2L + 2L = 0 0 + 6l + -2lx + xL = 0 + 2L 6l + -2lx + xL = 0 + 2L Remove the zero: 6l + -2lx + xL = 2L Add '-1xL' to each side of the equation. 6l + -2lx + xL + -1xL = 2L + -1xL Combine like terms: xL + -1xL = 0 6l + -2lx + 0 = 2L + -1xL 6l + -2lx = 2L + -1xL 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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