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