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Simplifying 3ln(x + -4) + 3x + -15 = 0 Reorder the terms: 3ln(-4 + x) + 3x + -15 = 0 (-4 * 3ln + x * 3ln) + 3x + -15 = 0 (-12ln + 3lnx) + 3x + -15 = 0 Reorder the terms: -15 + -12ln + 3lnx + 3x = 0 Solving -15 + -12ln + 3lnx + 3x = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + -12ln + 3lnx + 15 + 3x = 0 + 15 Reorder the terms: -15 + 15 + -12ln + 3lnx + 3x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -12ln + 3lnx + 3x = 0 + 15 -12ln + 3lnx + 3x = 0 + 15 Combine like terms: 0 + 15 = 15 -12ln + 3lnx + 3x = 15 Add '-3x' to each side of the equation. -12ln + 3lnx + 3x + -3x = 15 + -3x Combine like terms: 3x + -3x = 0 -12ln + 3lnx + 0 = 15 + -3x -12ln + 3lnx = 15 + -3x Reorder the terms: -15 + -12ln + 3lnx + 3x = 15 + -3x + -15 + 3x Reorder the terms: -15 + -12ln + 3lnx + 3x = 15 + -15 + -3x + 3x Combine like terms: 15 + -15 = 0 -15 + -12ln + 3lnx + 3x = 0 + -3x + 3x -15 + -12ln + 3lnx + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 -15 + -12ln + 3lnx + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -4ln + lnx + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -4ln + lnx + x)' equal to zero and attempt to solve: Simplifying -5 + -4ln + lnx + x = 0 Solving -5 + -4ln + lnx + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -4ln + lnx + 5 + x = 0 + 5 Reorder the terms: -5 + 5 + -4ln + lnx + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4ln + lnx + x = 0 + 5 -4ln + lnx + x = 0 + 5 Combine like terms: 0 + 5 = 5 -4ln + lnx + x = 5 Add '-1x' to each side of the equation. -4ln + lnx + x + -1x = 5 + -1x Combine like terms: x + -1x = 0 -4ln + lnx + 0 = 5 + -1x -4ln + lnx = 5 + -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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