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Simplifying lg(3x + -5) = lg(4 + -1x) Reorder the terms: gl(-5 + 3x) = lg(4 + -1x) (-5 * gl + 3x * gl) = lg(4 + -1x) (-5gl + 3glx) = lg(4 + -1x) -5gl + 3glx = (4 * gl + -1x * gl) -5gl + 3glx = (4gl + -1glx) Solving -5gl + 3glx = 4gl + -1glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4gl' to each side of the equation. -5gl + -4gl + 3glx = 4gl + -4gl + -1glx Combine like terms: -5gl + -4gl = -9gl -9gl + 3glx = 4gl + -4gl + -1glx Combine like terms: 4gl + -4gl = 0 -9gl + 3glx = 0 + -1glx -9gl + 3glx = -1glx Add 'glx' to each side of the equation. -9gl + 3glx + glx = -1glx + glx Combine like terms: 3glx + glx = 4glx -9gl + 4glx = -1glx + glx Combine like terms: -1glx + glx = 0 -9gl + 4glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(-9 + 4x) = 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 '(-9 + 4x)' equal to zero and attempt to solve: Simplifying -9 + 4x = 0 Solving -9 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x = 0 + 9 4x = 0 + 9 Combine like terms: 0 + 9 = 9 4x = 9 Add '-4x' to each side of the equation. 4x + -4x = 9 + -4x Combine like terms: 4x + -4x = 0 0 = 9 + -4x Simplifying 0 = 9 + -4x 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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