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Simplifying log(x + 4) + log(2x + 3) = log(1 + -2x) Reorder the terms: glo(4 + x) + log(2x + 3) = log(1 + -2x) (4 * glo + x * glo) + log(2x + 3) = log(1 + -2x) (4glo + glox) + log(2x + 3) = log(1 + -2x) Reorder the terms: 4glo + glox + glo(3 + 2x) = log(1 + -2x) 4glo + glox + (3 * glo + 2x * glo) = log(1 + -2x) 4glo + glox + (3glo + 2glox) = log(1 + -2x) Reorder the terms: 4glo + 3glo + glox + 2glox = log(1 + -2x) Combine like terms: 4glo + 3glo = 7glo 7glo + glox + 2glox = log(1 + -2x) Combine like terms: glox + 2glox = 3glox 7glo + 3glox = log(1 + -2x) 7glo + 3glox = (1 * glo + -2x * glo) 7glo + 3glox = (1glo + -2glox) Solving 7glo + 3glox = 1glo + -2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. 7glo + -1glo + 3glox = 1glo + -1glo + -2glox Combine like terms: 7glo + -1glo = 6glo 6glo + 3glox = 1glo + -1glo + -2glox Combine like terms: 1glo + -1glo = 0 6glo + 3glox = 0 + -2glox 6glo + 3glox = -2glox Add '2glox' to each side of the equation. 6glo + 3glox + 2glox = -2glox + 2glox Combine like terms: 3glox + 2glox = 5glox 6glo + 5glox = -2glox + 2glox Combine like terms: -2glox + 2glox = 0 6glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(6 + 5x) = 0Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Add '-5x' to each side of the equation. 5x + -5x = -6 + -5x Combine like terms: 5x + -5x = 0 0 = -6 + -5x Simplifying 0 = -6 + -5x 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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