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Simplifying log * 2(9x + 10) = log * 2(5x + 2) Reorder the terms: glo * 2(10 + 9x) = log * 2(5x + 2) Reorder the terms for easier multiplication: 2glo(10 + 9x) = log * 2(5x + 2) (10 * 2glo + 9x * 2glo) = log * 2(5x + 2) (20glo + 18glox) = log * 2(5x + 2) Reorder the terms: 20glo + 18glox = glo * 2(2 + 5x) Reorder the terms for easier multiplication: 20glo + 18glox = 2glo(2 + 5x) 20glo + 18glox = (2 * 2glo + 5x * 2glo) 20glo + 18glox = (4glo + 10glox) Solving 20glo + 18glox = 4glo + 10glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 20glo + -4glo + 18glox = 4glo + -4glo + 10glox Combine like terms: 20glo + -4glo = 16glo 16glo + 18glox = 4glo + -4glo + 10glox Combine like terms: 4glo + -4glo = 0 16glo + 18glox = 0 + 10glox 16glo + 18glox = 10glox Add '-10glox' to each side of the equation. 16glo + 18glox + -10glox = 10glox + -10glox Combine like terms: 18glox + -10glox = 8glox 16glo + 8glox = 10glox + -10glox Combine like terms: 10glox + -10glox = 0 16glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(2 + x) = 0 Ignore the factor 8.Subproblem 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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