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Simplifying lg(5x + 1) = lg(6 + -4x) Reorder the terms: gl(1 + 5x) = lg(6 + -4x) (1 * gl + 5x * gl) = lg(6 + -4x) (1gl + 5glx) = lg(6 + -4x) 1gl + 5glx = (6 * gl + -4x * gl) 1gl + 5glx = (6gl + -4glx) Solving 1gl + 5glx = 6gl + -4glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6gl' to each side of the equation. 1gl + -6gl + 5glx = 6gl + -6gl + -4glx Combine like terms: 1gl + -6gl = -5gl -5gl + 5glx = 6gl + -6gl + -4glx Combine like terms: 6gl + -6gl = 0 -5gl + 5glx = 0 + -4glx -5gl + 5glx = -4glx Add '4glx' to each side of the equation. -5gl + 5glx + 4glx = -4glx + 4glx Combine like terms: 5glx + 4glx = 9glx -5gl + 9glx = -4glx + 4glx Combine like terms: -4glx + 4glx = 0 -5gl + 9glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(-5 + 9x) = 0Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 '(-5 + 9x)' equal to zero and attempt to solve: Simplifying -5 + 9x = 0 Solving -5 + 9x = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 9x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 9x = 0 + 5 9x = 0 + 5 Combine like terms: 0 + 5 = 5 9x = 5 Add '-9x' to each side of the equation. 9x + -9x = 5 + -9x Combine like terms: 9x + -9x = 0 0 = 5 + -9x Simplifying 0 = 5 + -9x 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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