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