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Simplifying lg(2x + -5) = lg(1 + -1x) Reorder the terms: gl(-5 + 2x) = lg(1 + -1x) (-5 * gl + 2x * gl) = lg(1 + -1x) (-5gl + 2glx) = lg(1 + -1x) -5gl + 2glx = (1 * gl + -1x * gl) -5gl + 2glx = (1gl + -1glx) Solving -5gl + 2glx = 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. -5gl + -1gl + 2glx = 1gl + -1gl + -1glx Combine like terms: -5gl + -1gl = -6gl -6gl + 2glx = 1gl + -1gl + -1glx Combine like terms: 1gl + -1gl = 0 -6gl + 2glx = 0 + -1glx -6gl + 2glx = -1glx Add 'glx' to each side of the equation. -6gl + 2glx + glx = -1glx + glx Combine like terms: 2glx + glx = 3glx -6gl + 3glx = -1glx + glx Combine like terms: -1glx + glx = 0 -6gl + 3glx = 0 Factor out the Greatest Common Factor (GCF), '3gl'. 3gl(-2 + x) = 0 Ignore the factor 3.Subproblem 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 '(-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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