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Simplifying log(-2x + 5) + -1log(x + 4) = log(-11x + -2) Reorder the terms: glo(5 + -2x) + -1log(x + 4) = log(-11x + -2) (5 * glo + -2x * glo) + -1log(x + 4) = log(-11x + -2) (5glo + -2glox) + -1log(x + 4) = log(-11x + -2) Reorder the terms: 5glo + -2glox + -1glo(4 + x) = log(-11x + -2) 5glo + -2glox + (4 * -1glo + x * -1glo) = log(-11x + -2) 5glo + -2glox + (-4glo + -1glox) = log(-11x + -2) Reorder the terms: 5glo + -4glo + -2glox + -1glox = log(-11x + -2) Combine like terms: 5glo + -4glo = 1glo 1glo + -2glox + -1glox = log(-11x + -2) Combine like terms: -2glox + -1glox = -3glox 1glo + -3glox = log(-11x + -2) Reorder the terms: 1glo + -3glox = glo(-2 + -11x) 1glo + -3glox = (-2 * glo + -11x * glo) 1glo + -3glox = (-2glo + -11glox) Solving 1glo + -3glox = -2glo + -11glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. 1glo + 2glo + -3glox = -2glo + 2glo + -11glox Combine like terms: 1glo + 2glo = 3glo 3glo + -3glox = -2glo + 2glo + -11glox Combine like terms: -2glo + 2glo = 0 3glo + -3glox = 0 + -11glox 3glo + -3glox = -11glox Add '11glox' to each side of the equation. 3glo + -3glox + 11glox = -11glox + 11glox Combine like terms: -3glox + 11glox = 8glox 3glo + 8glox = -11glox + 11glox Combine like terms: -11glox + 11glox = 0 3glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(3 + 8x) = 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 '(3 + 8x)' equal to zero and attempt to solve: Simplifying 3 + 8x = 0 Solving 3 + 8x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8x = 0 + -3 8x = 0 + -3 Combine like terms: 0 + -3 = -3 8x = -3 Add '-8x' to each side of the equation. 8x + -8x = -3 + -8x Combine like terms: 8x + -8x = 0 0 = -3 + -8x Simplifying 0 = -3 + -8x 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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