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