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Simplifying lg(5x + -4) = lg(3x + -7) Reorder the terms: gl(-4 + 5x) = lg(3x + -7) (-4 * gl + 5x * gl) = lg(3x + -7) (-4gl + 5glx) = lg(3x + -7) Reorder the terms: -4gl + 5glx = gl(-7 + 3x) -4gl + 5glx = (-7 * gl + 3x * gl) -4gl + 5glx = (-7gl + 3glx) Solving -4gl + 5glx = -7gl + 3glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7gl' to each side of the equation. -4gl + 7gl + 5glx = -7gl + 7gl + 3glx Combine like terms: -4gl + 7gl = 3gl 3gl + 5glx = -7gl + 7gl + 3glx Combine like terms: -7gl + 7gl = 0 3gl + 5glx = 0 + 3glx 3gl + 5glx = 3glx Add '-3glx' to each side of the equation. 3gl + 5glx + -3glx = 3glx + -3glx Combine like terms: 5glx + -3glx = 2glx 3gl + 2glx = 3glx + -3glx Combine like terms: 3glx + -3glx = 0 3gl + 2glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(3 + 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -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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