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