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Simplifying lg(2x + -4) = lg(3x + 2) Reorder the terms: gl(-4 + 2x) = lg(3x + 2) (-4 * gl + 2x * gl) = lg(3x + 2) (-4gl + 2glx) = lg(3x + 2) Reorder the terms: -4gl + 2glx = gl(2 + 3x) -4gl + 2glx = (2 * gl + 3x * gl) -4gl + 2glx = (2gl + 3glx) Solving -4gl + 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. -4gl + -2gl + 2glx = 2gl + -2gl + 3glx Combine like terms: -4gl + -2gl = -6gl -6gl + 2glx = 2gl + -2gl + 3glx Combine like terms: 2gl + -2gl = 0 -6gl + 2glx = 0 + 3glx -6gl + 2glx = 3glx Add '-3glx' to each side of the equation. -6gl + 2glx + -3glx = 3glx + -3glx Combine like terms: 2glx + -3glx = -1glx -6gl + -1glx = 3glx + -3glx Combine like terms: 3glx + -3glx = 0 -6gl + -1glx = 0 Factor out the Greatest Common Factor (GCF), '-1gl'. -1gl(6 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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