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Simplifying lg(x + -8) + -1lg(3x + -4) = lg(x + -5) Reorder the terms: gl(-8 + x) + -1lg(3x + -4) = lg(x + -5) (-8 * gl + x * gl) + -1lg(3x + -4) = lg(x + -5) (-8gl + glx) + -1lg(3x + -4) = lg(x + -5) Reorder the terms: -8gl + glx + -1gl(-4 + 3x) = lg(x + -5) -8gl + glx + (-4 * -1gl + 3x * -1gl) = lg(x + -5) -8gl + glx + (4gl + -3glx) = lg(x + -5) Reorder the terms: -8gl + 4gl + glx + -3glx = lg(x + -5) Combine like terms: -8gl + 4gl = -4gl -4gl + glx + -3glx = lg(x + -5) Combine like terms: glx + -3glx = -2glx -4gl + -2glx = lg(x + -5) Reorder the terms: -4gl + -2glx = gl(-5 + x) -4gl + -2glx = (-5 * gl + x * gl) -4gl + -2glx = (-5gl + glx) Solving -4gl + -2glx = -5gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5gl' to each side of the equation. -4gl + 5gl + -2glx = -5gl + 5gl + glx Combine like terms: -4gl + 5gl = 1gl 1gl + -2glx = -5gl + 5gl + glx Combine like terms: -5gl + 5gl = 0 1gl + -2glx = 0 + glx 1gl + -2glx = glx Add '-1glx' to each side of the equation. 1gl + -2glx + -1glx = glx + -1glx Combine like terms: -2glx + -1glx = -3glx 1gl + -3glx = glx + -1glx Combine like terms: glx + -1glx = 0 1gl + -3glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(1 + -3x) = 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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Add '3x' to each side of the equation. -3x + 3x = -1 + 3x Combine like terms: -3x + 3x = 0 0 = -1 + 3x Simplifying 0 = -1 + 3x 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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