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Simplifying lg(5x + -2) = lg(2 + -5x) Reorder the terms: gl(-2 + 5x) = lg(2 + -5x) (-2 * gl + 5x * gl) = lg(2 + -5x) (-2gl + 5glx) = lg(2 + -5x) -2gl + 5glx = (2 * gl + -5x * gl) -2gl + 5glx = (2gl + -5glx) Solving -2gl + 5glx = 2gl + -5glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2gl' to each side of the equation. -2gl + -2gl + 5glx = 2gl + -2gl + -5glx Combine like terms: -2gl + -2gl = -4gl -4gl + 5glx = 2gl + -2gl + -5glx Combine like terms: 2gl + -2gl = 0 -4gl + 5glx = 0 + -5glx -4gl + 5glx = -5glx Add '5glx' to each side of the equation. -4gl + 5glx + 5glx = -5glx + 5glx Combine like terms: 5glx + 5glx = 10glx -4gl + 10glx = -5glx + 5glx Combine like terms: -5glx + 5glx = 0 -4gl + 10glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(-2 + 5x) = 0 Ignore the factor 2.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 + 5x)' equal to zero and attempt to solve: Simplifying -2 + 5x = 0 Solving -2 + 5x = 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 + 5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x = 0 + 2 5x = 0 + 2 Combine like terms: 0 + 2 = 2 5x = 2 Add '-5x' to each side of the equation. 5x + -5x = 2 + -5x Combine like terms: 5x + -5x = 0 0 = 2 + -5x Simplifying 0 = 2 + -5x 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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