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